Answered

Solve the system of equations below.

[tex]\[
\begin{array}{c}
4x + y = 16 \\
2x + 3y = -2
\end{array}
\][/tex]

A. [tex]\((5, -4)\)[/tex]
B. [tex]\((5, 4)\)[/tex]
C. [tex]\((4, -5)\)[/tex]
D. [tex]\((-5, 4)\)[/tex]



Answer :

GinnyAnswer
To solve the system of equations given:

[tex]\[ \begin{array}{c} 4x + y = 16 \\ 2x + 3y = -2 \end{array} \][/tex]

we need to find the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfy both equations simultaneously.

### Step-by-Step Solution:

1. Label the equations for convenience:

[tex]\[ \text{(1) } 4x + y = 16 \][/tex]
[tex]\[ \text{(2) } 2x + 3y = -2 \][/tex]

2. Express [tex]\(y\)[/tex] from equation (1):

[tex]\[ y = 16 - 4x \tag{3} \][/tex]

3. Substitute [tex]\(y\)[/tex] from equation (3) in equation (2):

[tex]\[ 2x + 3(16 - 4x) = -2 \][/tex]

Simplify and solve for [tex]\(x\)[/tex]:
[tex]\[ 2x + 48 - 12x = -2 \][/tex]
[tex]\[ 2x - 12x = -2 - 48 \][/tex]
[tex]\[ -10x = -50 \][/tex]
[tex]\[ x = 5 \][/tex]

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

[tex]\[ y = 16 - 4 \times 5 \][/tex]
[tex]\[ y = 16 - 20 \][/tex]
[tex]\[ y = -4 \][/tex]

### Conclusion:
The solution to the system of equations is [tex]\( x = 5 \)[/tex] and [tex]\( y = -4 \)[/tex]. Therefore, the correct answer is:

A. [tex]\((5, -4)\)[/tex].

Other Questions