Question

Solve using substitution.

4x + 5y = 6
x + y = 2

(
,
)

Answer 1

To solve the system of equations using substitution, follow these steps:

1. Solve one of the equations for one variable. We'll use the second equation:
\[
x + y = 2
\]
Rearranging gives us:
\[
x = 2 - y
\]

2. Substitute this expression for \( x \) into the first equation:
\[
4x + 5y = 6
\]
Substituting \( x = 2 - y \):
\[
4(2 - y) + 5y = 6
\]

3. Distribute and simplify:
\[
8 - 4y + 5y = 6
\]
Combining like terms yields:
\[
8 + y = 6
\]

4. Solve for \( y \):
\[
y = 6 - 8
\]
\[
y = -2
\]

5. Now substitute \( y = -2 \) back into the expression for \( x \):
\[
x = 2 - (-2)
\]
\[
x = 2 + 2
\]
\[
x = 4
\]

The solution to the system of equations is:
\[
(x, y) = (4, -2)
\]

So, the final answer is
\[
(4, -2)
\]