Question

The coordinate plane shows the graphs for the following system of equations.

y
=
−
8
x
−
63

y
=
0
.
25
x
−
3


image

Part A:

Identify the solution to this system of equations. Explain how you determined the solution.

Part B:

If the equation
y
=
0
.
25
x
+
3
is replaced with
y
=
−
0
.
25
x
−
1
, will the solution to the new system of equations be the same as in the original system? Explain your answer.

Answer 1

Part A

Set the two expressions for y equal to find the intersection:
-8x - 63 = 0.25x - 3
-8.25x = 60
x = 60 / -8.25 = -80/11 ≈ -7.27

y = 0.25x - 3 = 0.25(-80/11) - 3 = -20/11 - 33/11 = -53/11 ≈ -4.82

Solution: (x, y) = (-80/11, -53/11) (approximately (-7.27, -4.82)). This is the point where the two lines intersect.

Part B

Replace the second equation and solve:
-8x - 63 = -0.25x - 1
-7.75x = 62
x = 62 / -7.75 = -8
y = -0.25(-8) - 1 = 2 - 1 = 1

New solution: (-8, 1), which is different from (-80/11, -53/11). So no—the solution is not the same, because replacing the line changes the intersection point (different slope/intercept gives a different meeting point).