Solve.

Question

–8x + 7y = 18
3x − y = –10

Answer 1

To solve the system of equations:

1. $-8x+7y=18$ (Equation 1)
2. $3x-y=-10$ (Equation 2)

We can use the substitution or elimination method. Here, I'll use substitution. First, we solve Equation 2 for $y$:

$$y=3x+10$$

Now, substitute $y$ in Equation 1:

$$-8x+7(3x+10)=18$$

Distributing $7$:

$$-8x+21x+70=18$$

Combine like terms:

$$13x+70=18$$

Now, isolate $x$ by subtracting $70$ from both sides:

$$13x=18-70$$ $$13x=-52$$

Now, divide by $13$:

$$x=-4$$

Next, substitute $x=-4$ back into the expression for $y$:

$$y=3(-4)+10$$ $$y=-12+10$$ $$y=-2$$

Thus, the solution to the system of equations is:

$$x=-4,y=-2$$

We can write the solution as $(-4,-2)$.