Solve -8x - 9y = -10 with x = -10.

Understand the Problem

The question is asking to solve a system of equations for the variables x and y, given that x is already specified as -10. We will substitute this value into the first equation to find the value of y.

Answer

The solution is $(-10, 10)$.

Steps to Solve

Substituting x into the equation

We have the equation $-8x - 9y = -10$ and we know that $x = -10$.

Substituting $-10$ into the equation gives:

$$ -8(-10) - 9y = -10 $$

Calculating the value

Now, compute $-8(-10)$:

$$ 80 - 9y = -10 $$

Isolating y

Next, isolate $y$ by subtracting $80$ from both sides:

$$ -9y = -10 - 80 $$

This simplifies to:

$$ -9y = -90 $$

Solving for y

Now, divide both sides by $-9$ to find $y$:

$$ y = \frac{-90}{-9} = 10 $$

The solution to the system of equations is $(x, y) = (-10, 10)$.

More Information

In this problem, we found the value of $y$ after substituting the given value of $x$ into the equation. The equations of this type are common in algebra, where isolating variables helps in solving systems.

Tips

A common mistake might be miscalculating the multiplication or the sign during substitution. Double-checking arithmetic can help avoid errors.

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