To solve the given system of equations:
[tex]\[
\begin{array}{l}
y = -3x + 4 \\
-4x + y = -10
\end{array}
\][/tex]
We will use the substitution method. Here’s the step-by-step solution:
1. Extract the first equation:
[tex]\[
y = -3x + 4
\][/tex]
2. Substitute [tex]\( y \)[/tex] from the first equation into the second equation:
[tex]\[
-4x + y = -10
\][/tex]
Substituting [tex]\( y = -3x + 4 \)[/tex] into the second equation:
[tex]\[
-4x + (-3x + 4) = -10
\][/tex]
Simplify the equation:
[tex]\[
-4x - 3x + 4 = -10
\][/tex]
Combine like terms:
[tex]\[
-7x + 4 = -10
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
[tex]\[
-7x + 4 = -10
\][/tex]
Subtract 4 from both sides:
[tex]\[
-7x = -14
\][/tex]
Divide both sides by -7:
[tex]\[
x = 2
\][/tex]
4. Use the value of [tex]\( x \)[/tex] to find [tex]\( y \)[/tex]:
Substitute [tex]\( x = 2 \)[/tex] into the first equation [tex]\( y = -3x + 4 \)[/tex]:
[tex]\[
y = -3(2) + 4
\][/tex]
Simplify the calculation:
[tex]\[
y = -6 + 4
\][/tex]
[tex]\[
y = -2
\][/tex]
Hence, the solution to the system is [tex]\( (x, y) = (2, -2) \)[/tex].
Therefore, the correct answer is:
c. [tex]\((2, -2)\)[/tex]
