# How do you solve 2x-y=6 and x+y=-3?

May 12, 2018

$x = 1$
$y = - 4$

#### Explanation:

There are 3 ways to solve this. Here is one way:

Elimination:

Line them up:

$2 x - y = 6$
$x + y = - 3$

$2 x + x = 3 x$
$- y + y = 0$
$6 - 3 = 3$

Put it back into an equation:

$3 x = 3$

$x = 1$

Plug what x equals (1) into one of the previous equations:

(2•1)-y=6
$\left(- 2\right) - y = 6 - 2$
$- y = 4 \mathmr{and} y = - 4$

$1 + y = - 3$
$\left(- 1\right) + y = - 3 - 1$
$y = - 4$

May 12, 2018

$x = 1$

$y = - 4$

#### Explanation:

These are called simultaneous equations. Multiply both equations so they both have the same leading coefficient. Use the coefficient of $x$ in one equation to multiply the entire equation of the other one. Do this for both.

$\left[2 x - y = 6\right] \text{ } \times 1$
$\left[x + y = - 3\right] \text{ } \times 2$

Equals

$2 x - y = 6$
$2 x + 2 y = - 6$

Then subtract the two equations

$2 x - 2 x = 0$
$\left[- y\right] - \left[2 y\right] = - 3 y$
$6 - \left[- 6\right] = 12$

Result:

$- 3 y = 12$

Simplify:

$- y = 4$

so

$y = - 4$

Replace the $y$ in one of the equations with $- 4$ to solve for $x$.

$2 x - y = 6$

$2 x - \left(- 4\right) = 6$

$2 x + 4 = 6$

$2 x = 6 - 4$

$2 x = 2$

$x = 1$