# How do you solve the system 4x-2y=16, 4x+2y=24 using graphing?

Feb 14, 2017

$x = 5 \mathmr{and} y = 2$

#### Explanation:

Let us solve the linear system by :
$\text{ }$
Multiplying one of the equations by an integer to eliminate one of the unknowns.
$\text{ }$
$\text{ }$
Solve for one unknown.
$\text{ }$
Substitute the solution to find the second unknown.
$\text{ }$
Solving the given linear system:
$\text{ }$
$4 x - 2 y = 16$$\text{ } E q 1$
$\text{ }$
$4 x + 2 y = 24$$\text{ } E q 2$
$\text{ }$
In the given linear system the coefficients of $\text{ "y" }$in both equations are given opposites.

$\text{ }$
$E q 1 + E q 2$
$\text{ }$
$\Rightarrow 4 x \cancel{- 2 y} + 4 x \cancel{+ 2 y} = 16 + 24$
$\text{ }$
$\Rightarrow 8 x = 40$
$\text{ }$
$\text{ }$
"rArrx=40/8
$\text{ }$
$\Rightarrow \textcolor{red}{x = 5}$
$\text{ }$
Substitute the value of $\text{ "color(red)(x=5)" }$ in $\text{ "Eq1" }$ to find $\text{ } y$
$\text{ }$
$4 x - 2 y = 16$$\text{ } E q 1$
$\text{ }$
$\Rightarrow 4 \left(\textcolor{red}{5}\right) - 2 y = 16$
$\text{ }$
$\Rightarrow 20 - 2 y = 16$
$\text{ }$
$\Rightarrow - 2 y = 16 - 20$
$\text{ }$
$\Rightarrow - 2 y = - 4$
$\text{ }$
$\Rightarrow y = \frac{- 4}{- 2}$
$\text{ }$
$\Rightarrow \textcolor{red}{y = 2}$
$\text{ }$
Therefore, $x = 5 \mathmr{and} y = 2$