Question

Solve the system of equations using the substitution method
x+3y=9
x=y-7

Answer 1

To solve the system of equations using the substitution method, we have the following equations:

1) \( x + 3y = 9 \)

2) \( x = y - 7 \)

We can substitute the expression for \( x \) from the second equation into the first equation.

Substituting \( x = y - 7 \) into the first equation:

\[
(y - 7) + 3y = 9
\]

Now, combine like terms:

\[
y - 7 + 3y = 9 \\
4y - 7 = 9
\]

Next, we solve for \( y \) by adding 7 to both sides:

\[
4y = 16
\]

Now, divide by 4:

\[
y = 4
\]

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

\[
x = y - 7 \\
x = 4 - 7 \\
x = -3
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-3, 4)
\]

To summarize, the solution is \( x = -3 \) and \( y = 4 \).