Answered

Select the correct answer.

What is the solution to this system of equations?

[tex]
\begin{aligned}
x & = 12 - y \\
2x + 3y & = 29
\end{aligned}
[/tex]

A. [tex]x = 8, \, y = 4[/tex]
B. [tex]x = 6, \, y = 6[/tex]
C. [tex]x = 7, \, y = 5[/tex]
D. [tex]x = 9, \, y = 3[/tex]



Answer :

GinnyAnswer
Let us solve the system of equations step-by-step.

The system of equations is:
[tex]\[ \begin{aligned} x & = 12 - y \quad \text{(Equation 1)} \\ 2x + 3y & = 29 \quad \text{(Equation 2)} \end{aligned} \][/tex]

1. Substitute Equation 1 into Equation 2:

From Equation 1, we know that:
[tex]\[ x = 12 - y \][/tex]

Substitute [tex]\( x = 12 - y \)[/tex] into Equation 2:
[tex]\[ 2(12 - y) + 3y = 29 \][/tex]

2. Simplify the resulting equation:

Distribute the 2:
[tex]\[ 24 - 2y + 3y = 29 \][/tex]

Combine like terms ([tex]\(-2y + 3y\)[/tex]):
[tex]\[ 24 + y = 29 \][/tex]

Solve for [tex]\( y \)[/tex]:
[tex]\[ y = 29 - 24 \][/tex]
[tex]\[ y = 5 \][/tex]

3. Substitute [tex]\( y = 5 \)[/tex] back into Equation 1 to find [tex]\( x \)[/tex]:

Using Equation 1:
[tex]\[ x = 12 - y \][/tex]
Substituting [tex]\( y = 5 \)[/tex]:
[tex]\[ x = 12 - 5 \][/tex]
[tex]\[ x = 7 \][/tex]

Therefore, the solution to the system of equations is:
[tex]\[ x = 7, \quad y = 5 \][/tex]

Thus, the correct answer is:
C. [tex]\( x = 7, y = 5 \)[/tex]