Select the correct answer.

Solve the system of equations given below.

[tex]\[
\begin{array}{r}
y - 15 = 3x \\
-2x + 5y = -3
\end{array}
\][/tex]

A. [tex]\((-3, 6)\)[/tex]

B. [tex]\((-7, -6)\)[/tex]

C. [tex]\((-6, -3)\)[/tex]

D. [tex]\((-6, 3)\)[/tex]



Answer :

To solve the system of equations,

[tex]\[ \begin{array}{r} y-15=3x \quad \text{(1)} \\ -2x+5y=-3 \quad \text{(2)} \end{array} \][/tex]

we will follow a systematic approach.

First, solve Equation (1) for [tex]\( y \)[/tex]:

[tex]\[ y - 15 = 3x \][/tex]

Rearrange this to express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:

[tex]\[ y = 3x + 15 \][/tex]

Next, substitute [tex]\( y = 3x + 15 \)[/tex] into Equation (2):

[tex]\[ -2x + 5(3x + 15) = -3 \][/tex]

Now, solve for [tex]\( x \)[/tex]:

[tex]\[ -2x + 15x + 75 = -3 \][/tex]

Combine like terms:

[tex]\[ 13x + 75 = -3 \][/tex]

Subtract 75 from both sides:

[tex]\[ 13x = -3 - 75 \][/tex]

[tex]\[ 13x = -78 \][/tex]

Divide by 13:

[tex]\[ x = \frac{-78}{13} \][/tex]

[tex]\[ x = -6 \][/tex]

Next, substitute [tex]\( x = -6 \)[/tex] back into the equation [tex]\( y = 3x + 15 \)[/tex] to find [tex]\( y \)[/tex]:

[tex]\[ y = 3(-6) + 15 \][/tex]

[tex]\[ y = -18 + 15 \][/tex]

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

Thus, the solution to the system of equations is [tex]\( (x, y) = (-6, -3) \)[/tex].

Among the given options, the correct answer is:

C. [tex]\((-6, -3)\)[/tex]