91Ó°ÊÓ

Elimination method enables us to eliminate or get rid of one of the variable, so we can solve a more simplified equation.

Given system of equations:

$\begin{array}{c}4x+5y=20\\ 5x+4y=7\end{array}$

Multiply the first equation, $4x+5y=20$by 5 and second equation, $5x+4y=7$by 4.

Then subtract the equations to eliminate the x variable as follows:

localid="1648726261833" $\begin{array}{l}\underset{¯}{\begin{array}{c}4x+5y=20\\ 5x+4y=\text{ â¶Ä„â¶Ä„}7\end{array}}\text{ â¶Ä„}\begin{array}{c}\text{multiplyby5}→\\ \text{multiplyby4}→\end{array}\text{ â¶Ä„â¶Ä„ }\underset{¯}{\begin{array}{c}20x+25y=100\\ \underset{−}{20x}+\underset{−}{16y}=\text{ â¶Ä„â¶Ä„}\underset{−}{28}\end{array}}\\ \text{ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„}0x+\text{ â¶Ä„}9y=\text{ â¶Ä„â¶Ä„}72\end{array}$

Solve the equation $9y=72$for y:

$\begin{array}{c}9y=72\\ \frac{9y}{9}=\frac{72}{9}\text{ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„dividebothsidesby9}\\ y=8\end{array}$

Substitute $y=8$in $4x+5y=20$and solve for $x:$

So, the solution of the given system is $\left(x,y\right)=\left(-5,8\right)$.