Questions: Choose the correct answer. You are working with your friend who finds the solution of -x+2y=1 and -2x-3y=-12 to be (-1,0). Explain to your friend why the answer is incorrect. Your friend had the slopes correct for both the lines, but not the y-intercepts. Your friend had the wrong answer for both the slopes and the y-intercepts. Your friend had the y-intercepts correct for both the lines, but not the slopes.

Solution Steps

We can solve the system of equations by substitution or elimination. Here's the solution using elimination:

Multiply the first equation by -2:

2x - 4y = -2

Add this to the second equation:

-2x - 3y = -12

This gives:

-7y = -14

y = 2

Substitute y=2 into the first equation:

-x + 2(2) = 1

-x + 4 = 1

-x = -3

x = 3

So the correct solution is (3, 2).

The provided solution is (-1, 0). Let's check this against both equations:

Equation 1: -(-1) + 2(0) = 1, which simplifies to 1 = 1. This is correct.

Equation 2: -2(-1) - 3(0) = -12, which simplifies to 2 = -12. This is incorrect.

Since the given point lies on the line -x + 2y = 1, your friend correctly determined the properties of that line. However, the point doesn't lie on -2x - 3y = -12. Therefore, your friend did not correctly represent the second line. They have the correct y-intercept for the first equation but not the second.

Final Answer