Question

Solve the system of equations. {4y−12=10x2y−14=4x

Answer 1

To solve the system of equations given by:

1. \( 4y - 12 = 10x \)
2. \( 2y - 14 = 4x \)

Let's first rearrange each equation into a more standard form.

### From the first equation:
\[
4y - 10x = 12
\]

### From the second equation:
\[
2y - 4x = 14
\]

Now, we can simplify the second equation. Dividing the entire equation by 2 gives:
\[
y - 2x = 7
\]
or
\[
y = 2x + 7
\]

Now we can substitute this expression for \( y \) into the first equation:

Substituting \( y = 2x + 7 \) into the first equation:
\[
4(2x + 7) - 10x = 12
\]

Expanding:
\[
8x + 28 - 10x = 12
\]

Combining like terms:
\[
-2x + 28 = 12
\]

Now, isolate \( x \):
\[
-2x = 12 - 28
\]
\[
-2x = -16
\]
\[
x = 8
\]

Now, substitute \( x = 8 \) back into \( y = 2x + 7 \) to find \( y \):
\[
y = 2(8) + 7 = 16 + 7 = 23
\]

Thus, the solution to the system of equations is:
\[
\boxed{(8, 23)}
\]