Question

George solved the linear equation shown below.

2x – 3y = 6

Which equation has the same x-intercept as the one that George solved?

2x – 3y = 8

3x = 3y – 9

4x = 12 – 5y

5x – 5y = 10

Answer 1

To find the x-intercept of the equation George solved, we set \( y = 0 \) in the equation \( 2x - 3y = 6 \).

Substituting \( y = 0 \):
\[
2x - 3(0) = 6
\]
\[
2x = 6
\]
\[
x = 3
\]
So, the x-intercept of George's equation is \( 3 \).

Next, we'll find the x-intercepts of the other equations provided to see which one has the same x-intercept of \( 3 \).

1. For \( 2x - 3y = 8 \):
\[
2x - 3(0) = 8 \implies 2x = 8 \implies x = 4
\]

2. For \( 3x = 3y - 9 \):
Rearranging gives:
\[
3x + 9 = 3y \implies y = x + 3
\]
Setting \( y = 0 \):
\[
0 = x + 3 \implies x = -3
\]

3. For \( 4x = 12 - 5y \):
Rearranging gives:
\[
5y = 12 - 4x \implies y = \frac{12 - 4x}{5}
\]
Setting \( y = 0 \):
\[
0 = 12 - 4x \implies 4x = 12 \implies x = 3
\]

4. For \( 5x - 5y = 10 \):
Rearranging gives:
\[
5x = 5y + 10 \implies y = x - 2
\]
Setting \( y = 0 \):
\[
0 = x - 2 \implies x = 2
\]

Now we can summarize the x-intercepts:
- \( 2x - 3y = 8 \) → \( x = 4 \)
- \( 3x = 3y - 9 \) → \( x = -3 \)
- \( 4x = 12 - 5y \) → \( x = 3 \) (same as George's)
- \( 5x - 5y = 10 \) → \( x = 2 \)

The equation that has the same x-intercept as George's equation is:
\[
\boxed{4x = 12 - 5y}
\]