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Use the substitution method to solve the system of equations.

[tex]\[
\begin{array}{l}
2x + 3y = 12 \\
y = x - 1
\end{array}
\][/tex]

Sagot :

GinnyAnswer
To solve the system of equations using the substitution method, we start by expressing one variable in terms of the other using one of the given equations. In this case, equation 2 provides an expression for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:

1. Write equation 2:
[tex]\[ y = x - 1 \][/tex]

2. Substitute this expression for [tex]\( y \)[/tex] into equation 1, which is:
[tex]\[ 2x + 3y = 12 \][/tex]
Substituting [tex]\( y = x - 1 \)[/tex] into equation 1:
[tex]\[ 2x + 3(x - 1) = 12 \][/tex]

3. Distribute [tex]\( 3 \)[/tex] inside the parentheses:
[tex]\[ 2x + 3x - 3 = 12 \][/tex]

4. Combine like terms:
[tex]\[ 5x - 3 = 12 \][/tex]

5. Solve for [tex]\( x \)[/tex] by isolating [tex]\( x \)[/tex]:
[tex]\[ 5x - 3 + 3 = 12 + 3 \][/tex]
[tex]\[ 5x = 15 \][/tex]
[tex]\[ x = \frac{15}{5} \][/tex]
[tex]\[ x = 3 \][/tex]

6. Now that we have [tex]\( x \)[/tex], use equation 2 to find [tex]\( y \)[/tex]:
[tex]\[ y = x - 1 \][/tex]
Substitute [tex]\( x = 3 \)[/tex]:
[tex]\[ y = 3 - 1 \][/tex]
[tex]\[ y = 2 \][/tex]

Thus, the solution to the system of equations is:
[tex]\[ (x, y) = (3, 2) \][/tex]
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