Question

Math

Posted 3 months ago

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

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Answer from Sia

Posted 3 months ago

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.

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