# How do you solve the system 2x + y =2 and x -y =10?

Feb 29, 2016

You can either solve by substitution or elimination. I"ll solve for you by substitution.

#### Explanation:

Firstly, you must isolate a variable in one of the equations (your choice).

$2 x + y = 2$

$y = 2 - 2 x$

Plug this in for y in the other equation.

$x - \left(2 - 2 x\right) = 10$

#x - 2 + 2x = 10

$3 x = 12$

$x = 4$

$\left(4\right) - y = 10$

$- y = 6$

$y = - 6$

The solution set is $\left\{4 , - 6\right\}$. Note that the solution set must always be written in the form $\left\{x , y\right\}$, for graphing purposes.

Practice exercises:

1. Solve by substitution.

a) $2 x + y = - 9 , - x - 3 y = - 8$

b) $3 x + 2 y = 2 , - 4 x + 3 y = - 48$

2 . A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current?

Note: the formula for speed is $s = \frac{d}{t}$

Good luck!