Question

solve using substitution.
y = 2x + 3
3x + 2y = 12

Answer 1

To solve the system of equations using substitution, we start with the two equations:

1. \( y = 2x + 3 \) (equation 1)
2. \( 3x + 2y = 12 \) (equation 2)

We can substitute equation 1 into equation 2.

Substituting \( y \) in equation 2:

\[
3x + 2(2x + 3) = 12
\]

Now expand the equation:

\[
3x + 4x + 6 = 12
\]

Combine like terms:

\[
7x + 6 = 12
\]

Next, we isolate \( x \) by subtracting 6 from both sides:

\[
7x = 6
\]

Now, divide by 7:

\[
x = \frac{6}{7}
\]

Now that we have the value of \( x \), we can substitute it back into equation 1 to find \( y \):

\[
y = 2\left(\frac{6}{7}\right) + 3
\]

Calculating that gives:

\[
y = \frac{12}{7} + 3
\]
\[
y = \frac{12}{7} + \frac{21}{7}
\]

Combining the fractions:

\[
y = \frac{33}{7}
\]

Thus, the solution to the system of equations is:

\[
\left( x, y \right) = \left( \frac{6}{7}, \frac{33}{7} \right)
\]