# How do I solve this system algebraically?

## x-2y=10 2x+y=5

For simplicity let's use substitution. From equation 1 we get $y = \frac{x}{2} - 5$. From equation 2 we get $y = - 2 x + 5$ Since $y$ is the same in both equations this means we set both expressions for $y$ equal to each other to obtain $\frac{x}{2} - 5 = - 2 x + 5 R i g h t a r r o w \frac{5}{2} x = 10 R i g h t a r r o w x = 4$
Substituting back in we obtain $y = - 2 x + 5 = \left(- 2\right) \left(4\right) + 5 = - 8 + 5 = - 3$
So the answer is $\left(4 , - 3\right)$