Question

solve the following system of equations.
$x - 5y = 16$
$x + 6y = -17$

Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases} x - 5y = 16 \\ x + 6y = -17 \end{cases}$$

Subtract the first equation from the second equation:
$$(x + 6y)-(x - 5y)=-17 - 16$$
Simplify the left - hand side: $x+6y - x + 5y=11y$, and the right - hand side: $-33$. So we get $11y=-33$.

Step2: Solve for y

Divide both sides of the equation $11y = - 33$ by 11:
$$y=\frac{-33}{11}=-3$$

Step3: Substitute y into one of the original equations to solve for x

Substitute $y = - 3$ into the first equation $x-5y = 16$:
$$x-5\times(-3)=16$$
Simplify: $x + 15=16$. Then subtract 15 from both sides: $x=16 - 15 = 1$

Answer:

$x = 1$, $y=-3$