To solve the system of linear equations:
[tex]\[ 4x + y = 8 \][/tex]
[tex]\[ -3x - y = 0 \][/tex]
Let us solve it step-by-step.
First, we'll add the two equations together to eliminate [tex]\( y \)[/tex]. This can be done directly since the coefficients of [tex]\( y \)[/tex] in both equations are opposites ([tex]\(+ y\)[/tex] and [tex]\( - y \)[/tex]):
[tex]\[ (4x + y) + (-3x - y) = 8 + 0 \][/tex]
Simplify:
[tex]\[ 4x - 3x + y - y = 8 \][/tex]
[tex]\[ x = 8 \][/tex]
Now that we have [tex]\( x = 8 \)[/tex], substitute this value back into one of the original equations to solve for [tex]\( y \)[/tex]. We’ll use the first equation:
[tex]\[ 4x + y = 8 \][/tex]
Substitute [tex]\( x = 8 \)[/tex]:
[tex]\[ 4(8) + y = 8 \][/tex]
[tex]\[ 32 + y = 8 \][/tex]
Solve for [tex]\( y \)[/tex]:
[tex]\[ y = 8 - 32 \][/tex]
[tex]\[ y = -24 \][/tex]
Thus, the solution to the system of equations is:
[tex]\[ x = 8 \][/tex]
[tex]\[ y = -24 \][/tex]
Therefore, the correct answer is [tex]\( (8, -24) \)[/tex].
