Linear Equations In Two Variables Quiz Questions And Answers
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Have you performed well during the linear equations class during school? Let's find it out with linear equations in two variables quiz questions and answers. When it comes to algebra, there are a lot of things to learn. If you think you have learned everything about the two variable linear equations, take this quiz. It will be an easy quiz for you. Just go and ace the quiz! All the best! Do not forget to share the quiz with other mathematicians.
- 1.
The linear equation 4x – 10y = 14 has:
- A.
A unique solution
- B.
Two solutions
- C.
Infinitely many solutions
- D.
No solutions
Correct Answer
C. Infinitely many solutionsExplanation
The given linear equation has infinitely many solutions because it represents a straight line with a slope of 4/10 and a y-intercept of -14/10. This means that for every value of x, there will be a corresponding value of y that satisfies the equation. In other words, there are an infinite number of points that lie on the line and satisfy the equation.Rate this question:
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- 2.
The equation 2x – 3y = 5 has a unique solution if x and y are:
- A.
Natural numbers
- B.
Positive real numbers
- C.
Real numbers
- D.
Rational numbers
Correct Answer
A. Natural numbersExplanation
The equation 2x – 3y = 5 has a unique solution if x and y are natural numbers. This means that x and y must be positive integers. If x and y were any other type of number, such as positive real numbers, real numbers, or rational numbers, there would be an infinite number of solutions to the equation. Therefore, the only way for the equation to have a unique solution is if x and y are natural numbers.Rate this question:
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- 3.
If (2, 0) is a solution of the linear equation 2x +3y = k, then the value of k is:
- A.
4
- B.
6
- C.
5
- D.
2
Correct Answer
A. 4Explanation
Since (2, 0) is a solution to the equation 2x + 3y = k, we can substitute the values of x and y into the equation. Plugging in x = 2 and y = 0, we get 2(2) + 3(0) = k, which simplifies to 4 = k. Therefore, the value of k is 4.Rate this question:
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- 4.
The graph of the linear equation 2x +3y = 6 cuts the y-axis at the point:
- A.
(2, 0)
- B.
(0, 3)
- C.
(3, 0)
- D.
(0, 2)
Correct Answer
D. (0, 2)Explanation
The linear equation 2x + 3y = 6 can be rewritten as 3y = -2x + 6. To find the point where the graph cuts the y-axis, we set x = 0 and solve for y. Plugging in x = 0 into the equation, we get 3y = 6, which gives y = 2. Therefore, the graph cuts the y-axis at the point (0, 2).Rate this question:
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- 5.
The equation y = 5, in two variables, can be written as:
- A.
1 . x + 1 . y = 5
- B.
0 . x + 0 . y = 5
- C.
1 . x + 0 . y = 5
- D.
0 . x + 1 . y = 5
Correct Answer
D. 0 . x + 1 . y = 5Explanation
The equation y = 5 represents a linear equation in two variables, x and y. In this equation, the coefficient of x is 0, which means that x does not affect the value of y. On the other hand, the coefficient of y is 1, indicating that y is equal to 5. Therefore, the equation 0 . x + 1 . y = 5 correctly represents the given equation y = 5.Rate this question:
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- 6.
Any point on the line y = x is of the form:
- A.
(a, –a)
- B.
(0, a)
- C.
(a, 0)
- D.
(a, a)
Correct Answer
D. (a, a)Explanation
Any point on the line y = x has the same x and y coordinates, which means that the x-coordinate and y-coordinate are equal. Therefore, the correct answer is (a, a).Rate this question:
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- 7.
The graph of x = 5 is a line:
- A.
Parallel to the x-axis at a distance 5 units from the origin
- B.
Parallel to the y-axis at a distance 5 units from the origin
- C.
Making an intercept 5 on the x-axis
- D.
Making an intercept 5 on the y-axis
Correct Answer
B. Parallel to the y-axis at a distance 5 units from the originExplanation
The correct answer is "Parallel to the y-axis at a distance 5 units from the origin." This is because the equation x = 5 represents a vertical line that is parallel to the y-axis. The line intersects the y-axis at the point (5,0) and is located 5 units to the right of the origin.Rate this question:
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- 8.
x = 9, y = 4 is a solution of the linear equation:
- A.
2x + y = 17
- B.
X + y = 17
- C.
X + 2y = 17
- D.
3x – 2y = 17
Correct Answer
C. X + 2y = 17Explanation
The given equation is x + 2y = 17. To check if x = 9 and y = 4 is a solution, we substitute these values into the equation.
9 + 2(4) = 17
9 + 8 = 17
17 = 17
Since the equation is true when x = 9 and y = 4, the answer x + 2y = 17 is correct.Rate this question:
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- 9.
Any point on the x-axis is of the form:
- A.
(0, y)
- B.
(x, 0)
- C.
(x, x)
- D.
(x, y)
Correct Answer
B. (x, 0)Explanation
The correct answer is (x, 0) because any point on the x-axis has a y-coordinate of 0. The x-coordinate can be any real number, but the y-coordinate will always be 0. Therefore, the correct form for any point on the x-axis is (x, 0).Rate this question:
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- 10.
If a linear equation has solutions (–3, 3), (0, 0), and (3, –3), then it is of the form:
- A.
Y – x = 0
- B.
X + y = 0
- C.
–2x + y = 0
- D.
–x + 2y = 0
Correct Answer
B. X + y = 0Explanation
To find the form of the linear equation given the solutions (-3, 3), (0, 0), and (3, -3), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
From the given solutions:
(-3, 3): x1 = -3, y1 = 3
(0, 0): x1 = 0, y1 = 0
(3, -3): x1 = 3, y1 = -3
First, let's find the slope using the points (-3, 3) and (0, 0): m = (y2 - y1) / (x2 - x1) m = (0 - 3) / (0 - (-3)) m = -3 / 3 m = -1
Now that we have the slope, we can plug it into the point-slope form for each point to determine the correct equation:
For point (-3, 3): y - 3 = -1(x - (-3)) y - 3 = -1(x + 3) y - 3 = -x - 3 y = -x
For point (0, 0): y - 0 = -1(x - 0) y = -x
For point (3, -3): y - (-3) = -1(x - 3) y + 3 = -x + 3 y = -x
Thus, the equation in the form that fits all the given points is: y = -x
Therefore, the correct option is: x + y = 0Rate this question:
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- 11.
The graph of the linear equation 5x + 3y = 10 is a line that meets the x-axis at the point:
- A.
(0, 3)
- B.
(3, 0)
- C.
(2, 0)
- D.
(0, 2)
Correct Answer
C. (2, 0)Explanation
The graph of a linear equation is a straight line. To find the point where the line intersects the x-axis, we need to find the x-coordinate of that point. We can do this by setting y=0 in the equation and solving for x. In this case, when y=0, the equation becomes 5x + 3(0) = 10, which simplifies to 5x = 10. Dividing both sides by 5 gives x = 2. Therefore, the point where the line meets the x-axis is (2, 0).Rate this question:
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- 12.
The positive solutions of the equation ax + by + c = 0 always lie in the:
- A.
Ist quadrant
- B.
2nd quadrant
- C.
3rd quadrant
- D.
4th quadrant
Correct Answer
A. Ist quadrantExplanation
The positive solutions of the equation ax + by + c = 0 always lie in the first quadrant because in the first quadrant, both x and y values are positive. Since the equation is linear, the values of x and y can only be positive in order to satisfy the equation. Therefore, the positive solutions will always be in the first quadrant.Rate this question:
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- 13.
The point of the form (a, –a) always lies on the line:
- A.
X = a
- B.
Y = –a
- C.
Y = x
- D.
X + y = 0
Correct Answer
D. X + y = 0 -
- 14.
The graph of x = 9 is a straight line:
- A.
Intersecting both the axes
- B.
Parallel to y-axis
- C.
Parallel to x-axis
- D.
Passing through the origin
Correct Answer
B. Parallel to y-axisExplanation
The graph of x = 9 is a straight line parallel to the y-axis because the equation x = 9 means that the value of x is always 9 regardless of the value of y. This means that all points on the graph will have an x-coordinate of 9 and can have any y-coordinate. Therefore, the graph will be a vertical line parallel to the y-axis.Rate this question:
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- 15.
The equation of the line parallel to the x-axis and six units above the origin is:
- A.
X = 6
- B.
X = –6
- C.
Y = 6
- D.
Y = –6
Correct Answer
C. Y = 6Explanation
The equation of a line parallel to the x-axis means that the line will have a constant y-value regardless of the x-value. Since the line is six units above the origin, the y-value will be 6. Therefore, the equation of the line parallel to the x-axis and six units above the origin is y = 6.Rate this question:
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Aug 20, 2024Quiz Edited by
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Expert Reviewed by
Janaisa Harris -
Dec 06, 2014Quiz Created by
Tanmay Shankar
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