# How do you complete the ordered pairs so that each ordered pair satisfies the given equation (3, a), (b, -1), 4x - 3y = 7?

Oct 6, 2015

$\left(3 , \textcolor{red}{a}\right) = \left(3 , \textcolor{red}{\frac{5}{3}}\right)$
and $\left(\textcolor{b l u e}{b} , - 1\right) = \left(\textcolor{b l u e}{1} , - 1\right)$

#### Explanation:

Given $4 x - 3 y = 7$

Point 1
If $\left(x , y\right) = \left(3 , a\right)$
$\textcolor{w h i t e}{\text{XXX}} 4 \left(3\right) - 3 \left(a\right) = 7$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow 12 - 3 a = 7$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow - 3 a = - 5$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow a = \frac{5}{3}$

Point 2
if $\left(x , y\right) = \left(b , - 1\right)$
$\textcolor{w h i t e}{\text{XXX}} 4 \left(b\right) - 3 \left(- 1\right) = 7$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow 4 b + 3 = 7$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow 4 b = 4$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow b = 1$