Solve using substitution.

Question

x+2y=7
2x-y=-16

Answer 1

To solve the system of equations using substitution, we start with the two given equations:

1. $x+2y=7$ (Equation 1)
2. $2x-y=-16$ (Equation 2)

First, solve Equation 1 for $x$:

$$x=7-2y$$

Now that we have $x$ in terms of $y$, we can substitute this expression for $x$ into Equation 2:

$$2(7-2y)-y=-16$$

Now distribute the $2$:

$$14-4y-y=-16$$

Combine like terms:

$$14-5y=-16$$

Next, isolate $y$ by subtracting 14 from both sides:

$$-5y=-16-14$$ $$-5y=-30$$

Now, divide both sides by -5:

$$y=\frac{-30}{-5}=6$$

Now that we have the value of $y$, we can substitute it back into the expression we found for $x$:

$$x=7-2(6)$$ $$x=7-12$$ $$x=-5$$

Thus, the solution to the system of equations is

$$x=-5,y=6$$

So the final answer is:

$$\boxed{{\displaystyle (-5,6)}}$$