Solve the system of equations.
$$
\begin{array}{l}
-12 x-5 y=40 \
12 x-11 y=88 \
x=\square \
y=\square
\end{array}
$$

Question

Solve the system of equations.
$$
\begin{array}{l}
-12 x-5 y=40 \
12 x-11 y=88 \
x=\square \
y=\square
\end{array}
$$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To solve the system of equations, we can use the method of elimination or substitution. Since the coefficients of x in both equations are opposites, we can add the equations to eliminate x. ‖ ‖ step 2 ⋮ Adding the two equations: $(-12x - 5y) + (12x - 11y) = 40 + 88$ ‖ ‖ step 3 ⋮ Simplifying the equation: $-16y = 128$ ‖ ‖ step 4 ⋮ Dividing both sides by $-16$ to solve for y: $y = \frac{128}{-16}$ ‖ ‖ step 5 ⋮ Calculating the value of y: $y = -8$ ‖ ‖ step 6 ⋮ Substitute $y = -8$ into one of the original equations to solve for x. Using the first equation: $-12x - 5(-8) = 40$ ‖ ‖ step 7 ⋮ Simplifying the equation: $-12x + 40 = 40$ ‖ ‖ step 8 ⋮ Subtracting 40 from both sides: $-12x = 0$ ‖ ‖ step 9 ⋮ Dividing both sides by $-12$ to solve for x: $x = 0$ ‖ ∻Answer∻ ⚹ $x = 0$ and $y = -8$ ⚹ ∻Key Concept∻ ⚹Solving a system of linear equations using elimination⚹ ∻Explanation∻ ⚹By adding the two equations, we eliminated the variable x, which allowed us to solve for y. Then we substituted the value of y back into one of the original equations to find the value of x.⚹◊What is the method for solving a system of equations involving two variables using substitution?⍭ Generate me a similar question◊

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