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What is the solution to the system of equations
[tex]\[
\left\{
\begin{array}{l}
3x + y = -18 \\
5x + 3y = 2
\end{array}
\right.
\][/tex]

A. (5, 33)

B. (-14, 24)

C. (-4, -6)

D. (-5, -3)

E. (4, -30)

F. (14, 60)



Answer :

GinnyAnswer
To solve the system of equations below:

[tex]\[ \begin{cases} 3x + y = -18 \\ 5x + 3y = 2 \end{cases} \][/tex]

we need to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that satisfy both equations simultaneously. Here is the step-by-step process:

1. Equation 1:
[tex]\[ 3x + y = -18 \][/tex]

2. Equation 2:
[tex]\[ 5x + 3y = 2 \][/tex]

Let’s start by isolating [tex]\( y \)[/tex] in the first equation:

[tex]\[ y = -18 - 3x \][/tex]

Next, we substitute this expression for [tex]\( y \)[/tex] into the second equation:

[tex]\[ 5x + 3(-18 - 3x) = 2 \][/tex]

Simplify the equation:

[tex]\[ 5x - 54 - 9x = 2 \][/tex]

Combine like terms:

[tex]\[ -4x - 54 = 2 \][/tex]

Add 54 to both sides:

[tex]\[ -4x = 56 \][/tex]

Divide both sides by -4:

[tex]\[ x = -14 \][/tex]

Now that we have [tex]\( x = -14 \)[/tex], we substitute this back into the expression for [tex]\( y \)[/tex]:

[tex]\[ y = -18 - 3(-14) \][/tex]

Calculate the result:

[tex]\[ y = -18 + 42 \][/tex]
[tex]\[ y = 24 \][/tex]

Therefore, the solution to the system of equations is:

[tex]\[ x = -14 \][/tex]
[tex]\[ y = 24 \][/tex]

So, the solution is [tex]\((-14, 24)\)[/tex], which corresponds to one of the given choices.

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