Question

1. which point lies on both $y = 5x - 3$ and $y = -4x + 6$? *

a. $(1, 2)$

b. $(2, 6)$

c. $(3, 1)$

d. $(4, 14)$

e. $(3, 10)$

Explanation:

Step1: Solve the system of equations

We have two equations: \( y = 5x - 3 \) and \( y=-4x + 6 \). Since both equal \( y \), we can set them equal to each other:
\( 5x - 3=-4x + 6 \)
Add \( 4x \) to both sides:
\( 5x+4x - 3=-4x+4x + 6 \)
\( 9x - 3 = 6 \)
Add 3 to both sides:
\( 9x - 3+3 = 6+3 \)
\( 9x=9 \)
Divide both sides by 9:
\( x = 1 \)

Step2: Find the value of \( y \)

Substitute \( x = 1 \) into \( y = 5x - 3 \):
\( y=5(1)-3=5 - 3 = 2 \)
So the solution to the system is \( (1,2) \), which means the point \( (1,2) \) lies on both lines. We can also verify by plugging \( (1,2) \) into the second equation: \( 2=-4(1)+6=-4 + 6 = 2 \), which is true.

Answer:

A. (1, 2)