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Linear Equations and Inequalities in Two Variables Quiz

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#1

Which of the following equations represents a linear equation in two variables?

3x - 2y = 5
Explanation

Linear equation with variables raised to the first power only.

#2

What is the solution to the linear equation 2x - 3y = 6?

(2, 0)
Explanation

Coordinates that satisfy the equation.

#3

Which of the following represents a vertical line?

x = 4
Explanation

Equation indicating a line parallel to the y-axis.

#4

What is the y-intercept of the line given by the equation 4y = 8x - 16?

(0, 4)
Explanation

Point where the line intersects the y-axis.

#5

What is the slope-intercept form of the equation 3x + 2y = 8?

y = -3/2x + 4
Explanation

Equation in the form y = mx + b.

#6

Which of the following inequalities represents a shaded region above the line?

y > 3x + 2
Explanation

Inequality indicating a region above a line on a coordinate plane.

#7

What is the slope of the line passing through the points (2, 5) and (4, 9)?

3
Explanation

Rate of vertical change between the two points.

#8

Which of the following represents a solution to the system of linear equations: 3x - y = 5 and x + 2y = 8?

(1, 2)
Explanation

Point satisfying both equations simultaneously.

#9

What is the solution set to the inequality 2x + 3y < 6?

{(x, y) | x + y < 2}
Explanation

Set of coordinates satisfying the inequality.

#10

What is the solution to the system of equations: 2x + 3y = 7 and x - 2y = 3?

(2, 1)
Explanation

Point satisfying both equations simultaneously.

#11

Which of the following systems of linear inequalities is represented by the shaded region below?

y > -x + 3 ; y ≤ 2x + 4
Explanation

System describing the region below two lines.

#12

What is the solution to the system of inequalities: y > 2x - 1 and y ≤ -x + 4?

{(x, y) | x > 1, y > 1}
Explanation

Region where both inequalities overlap.

#13

Which of the following represents the solution set to the inequality system: x + y ≤ 4 and x - y > 1?

{(x, y) | x ≤ 2, y ≤ 2, x > 1}
Explanation

Set of coordinates satisfying both inequalities.

#14

What is the solution to the inequality system: y < 2x + 1 and y > -x + 3?

{(x, y) | x > -1, y < 1}
Explanation

Region where both inequalities overlap.

#15

What is the slope of the line perpendicular to the line with equation y = -2x + 4?

-1/2
Explanation

Negative reciprocal of the slope of the given line.

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