The equations y = 2 3 x + 5 and y = -x − 5 are graphed below.

According to the graph, what are the values of x and y that simultaneously satisfy both of these linear equations?

A. (0, 5)
Incorrect. This ordered pair is the y-intercept of the first equation. The values of x and y that simultaneously satisfy both of the linear equations are found in the coordinates of the point of intersection of the two lines.

B. (1, -6)
Incorrect. To write an ordered pair, read the x-coordinate first.

C. (6, 1)
Incorrect. The intersection of the two lines represents the solution to the equation, and the intersection lies in Quadrant II. The x-values in Quadrant II must be negative.

D. (-6, 1)
Correct!

Three lines are graphed below: y = 2x − 3, y = -x + 3, and y = 0.5x − 6.

Which two equations have a simultaneous solution of (6, -3)?

A. y = −x + 3 and y = 0.5x − 6
Correct!

B. y = 2x − 3 and y = -x + 3
Incorrect. These two lines intersect at (2, 1), not (6, -3).

C. y = 0.5x – 6 and y = 2x – 3
Incorrect. These two lines intersect at (-2, -7), not (6, -3).

D. Not here
Incorrect. Locate two lines that intersect at the point (6, -3).

The equations y = 1 4 x − 4 and y = -3x + 9 are graphed below.

According to the graph, what are the values of x and y that simultaneously satisfy both of these linear equations?

A. (-3, 4)
Incorrect. To write an ordered pair, read the x-coordinate first.

B. (4, -3)
Correct!

C. (0, -4)
Incorrect. This ordered pair is the y-intercept of the equation y = 1 4 x − 4.

D. (3, 0)
Incorrect. This ordered pair is the x-intercept of the equation y = -3x + 9.

Shayne graphed the equations y = 2x and y = 0.25x − 7 below.

How can Shayne verify that (-4, -8) is the simultaneous solution to both of these equations?

A. Substitute x = -8 and y = -4 into both equations, and use the order of operations to determine if the resulting equations are both true.
Incorrect. The two lines intersect at the point (-4, -8), indicating that the simultaneous solution is x = -4 and y = -8.

B. Substitute x = -4 and y = -8 into both equations, and use the order of operations to determine if the resulting equations are both true.
Correct!

C. Substitute the coordinates of the y-intercepts of each equation into their respective equation. Simplify and verify that the resulting equations are both true.
Incorrect. Using the y-intercepts will give one solution for each equation but not the simultaneous solution to both equations.

D. Substitute the coordinates of the x-intercepts of each equation into their respective equation. Simplify and verify that the resulting equations are both true.
Incorrect. Using the x-intercepts will give one solution for each equation but not the simultaneous solution to both equations.

What is the simultaneous solution to the linear equations y = 0.6x − 4 and y = -x + 4?

A. (-4, 4)
Incorrect. Graph each equation, and determine the coordinates of the intersection point.

B. (0, 4)
Incorrect. Graph each equation, and determine the coordinates of the intersection point.

C. (5, -1)
Correct!

D. (-1, 5)
Incorrect. When representing a solution as an ordered pair, list x first: (x, y).