Question

Solve the system: y = x - 5 y = -3x 7 what is the point of intersection? ( x , y )

a) (-2, 5)
b) (3, -2)
c) (1, 3)
d) (1, -2)

Answer 1

The system of equations y = x - 5 and y = -3x + 7 is solved by setting them equal to each other, solving for x, and then substituting back to find y. The point of intersection for these lines is (3, -2).

Step-by-step explanation:

To solve the system of equations given as y = x - 5 and y = -3x + 7, we can set the two equations equal to each other since they both equal y:

x - 5 = -3x + 7

Add 3x to both sides to get:

4x - 5 = 7

Then add 5 to both sides:

4x = 12

Divide by 4 to find x:

x = 3

Substitute x back into either equation to find y:

y = (3) - 5

y = -2

Thus, the point of intersection is (3, -2), which corresponds to answer choice (b).