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On your own paper, solve the system of equations using substitution and identify the solution.

[tex]\[
\begin{array}{l}
x + 2y = 1 \\
5x + 3y = -23
\end{array}
\][/tex]

Note: Be sure to format your answer correctly as (x, y).

Sagot :

GinnyAnswer
To solve the system of equations using the substitution method, we will follow these steps:

1. Express [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex] using the first equation:

[tex]\( x + 2y = 1 \)[/tex]

Solve for [tex]\( x \)[/tex]:
[tex]\[ x = 1 - 2y \][/tex]

2. Substitute [tex]\( x = 1 - 2y \)[/tex] into the second equation:

The second equation is [tex]\( 5x + 3y = -23 \)[/tex]. Substitute [tex]\( x \)[/tex]:
[tex]\[ 5(1 - 2y) + 3y = -23 \][/tex]

3. Simplify and solve for [tex]\( y \)[/tex]:
[tex]\[ 5 \cdot 1 - 5 \cdot 2y + 3y = -23 \][/tex]
[tex]\[ 5 - 10y + 3y = -23 \][/tex]
[tex]\[ 5 - 7y = -23 \][/tex]
Subtract 5 from both sides:
[tex]\[ -7y = -23 - 5 \][/tex]
[tex]\[ -7y = -28 \][/tex]
Divide both sides by -7:
[tex]\[ y = \frac{-28}{-7} \][/tex]
[tex]\[ y = 4 \][/tex]

4. Substitute [tex]\( y = 4 \)[/tex] back into the expression for [tex]\( x \)[/tex]:
[tex]\[ x = 1 - 2y \][/tex]
[tex]\[ x = 1 - 2 \cdot 4 \][/tex]
[tex]\[ x = 1 - 8 \][/tex]
[tex]\[ x = -7 \][/tex]

Thus, the solution to the system of equations is:
[tex]\[ (x, y) = (-7, 4) \][/tex]
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