Question

6y−7=x
3x−8y=−31

Answer 1

To solve the system of equations given by

1. \( 6y - 7 = x \)
2. \( 3x - 8y = -31 \)

we can use substitution. First, let's express \( x \) in terms of \( y \) from the first equation:

\[
x = 6y - 7
\]

Now, we'll substitute this expression for \( x \) into the second equation:

\[
3(6y - 7) - 8y = -31
\]

Expanding this equation:

\[
18y - 21 - 8y = -31
\]

Combining like terms:

\[
10y - 21 = -31
\]

Now, add 21 to both sides:

\[
10y = -31 + 21
\]

\[
10y = -10
\]

Now, divide by 10:

\[
y = -1
\]

Now that we have the value of \( y \), we can substitute it back into the first equation to find \( x \):

\[
x = 6(-1) - 7
\]

\[
x = -6 - 7
\]

\[
x = -13
\]

Therefore, the solution to the system of equations is:

\[
(x, y) = (-13, -1)
\]

You can verify this solution by plugging \( x \) and \( y \) back into the original equations to confirm that both are satisfied.

1. For \( 6y - 7 = x \):

\[
6(-1) - 7 = -6 - 7 = -13 \quad \text{(satisfied)}
\]

2. For \( 3x - 8y = -31 \):

\[
3(-13) - 8(-1) = -39 + 8 = -31 \quad \text{(satisfied)}
\]

Thus, the solution \( (x, y) = (-13, -1) \) is indeed correct.