# How do you find an ordered pair for -7x + 6y = 11 and 8x - 3y = -1?

May 17, 2017

$x = 1 \mathmr{and} y = 3$
$\left(1 , 3\right)$

#### Explanation:

"Find an ordered pair" means find $\left(x , y\right)$, which in other words means, solve the system of equations.

The ideal situation is to have one of the variables in the two equations as additive inverses.
Notice that the $y$-terms already have opposite signs.

$- 7 x \textcolor{b l u e}{+ 6 y} = 11 \mathmr{and} 8 x \textcolor{b l u e}{- 3 y} = - 1$

Multipying the second equation by $2$ will give $- 6 y$

$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots . .} - 7 x + 6 y = \text{ } 11$......................A
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots .} 8 x - 3 y = - 1$.......................B

$B \times 2 : \textcolor{w h i t e}{\ldots . .} 16 x - 6 y = - 2$......................C
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots . .} - 7 x + 6 y = \text{ } 11$......................A

$A + C : \textcolor{w h i t e}{\ldots . .} 9 x = 9$
$A + C : \textcolor{w h i t e}{\ldots \ldots} x = 1$

Substitute #x=1 into A (or any other equation.

$- 7 \left(1\right) + 6 y = 11$

$6 y = 11 + 7$
$6 y = 18$
$y = 3$

Check in B:

Is $8 \left(1\right) - 3 \left(3\right) = - 1$?
$\text{ } 8 - 9$
$= - 1$
.