Question

Write and solve a system of equations for the graph shown.
2
4
6
2
4
6
x
y



x y graph
Question content area bottom
Part 1
Which of the following represents the system of equations shown in the​ graph?
A.y equals negative three halves x plus 7 y equals 6 minus x
y equals negative three halves x plus 7
y equals 6 minus x
B.y equals two thirds x plus 1 y equals 6 minus x
y equals two thirds x plus 1
y equals 6 minus x
C.y equals two thirds x plus 1 y equals one half x plus 1
y equals two thirds x plus 1
y equals one half x plus 1
D.y equals negative three halves x plus 7 y equals one half x plus 1
y equals negative three halves x plus 7
y equals one half x plus 1

Answer 1

Answer: A.

The system is
y = (-3/2)x + 7
y = 6 − x.

Solve by equating:
(-3/2)x + 7 = 6 − x
⇒ (-3/2 + 1)x = −1
⇒ (−1/2)x = −1
⇒ x = 2.

Then y = 6 − 2 = 4. Solution: (2, 4).