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:

Multiply the first equation, $6x+y=15$by 4 and add the new resultant equation to the equation is $x-4y=-10$.

$\begin{array}{l}\underset{¯}{\begin{array}{c}6x+y=\text{ â¶Ä„â¶Ä„}15\\ x−4y=−10\end{array}}\text{ â¶Ä„}\begin{array}{c}\text{multiplyby4}→\\ \end{array}\text{ â¶Ä„â¶Ä„ }\underset{¯}{\begin{array}{c}24x+4y=\text{ â¶Ä„â¶Ä„}60\\ x−4y=−10\end{array}}\\ \text{ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„}25x+0y=\text{ â¶Ä„â¶Ä„}50\end{array}$

Solve the equation $25x=50$for x:

$\begin{array}{c}25x=50\\ \frac{25x}{25}=\frac{50}{25}\text{ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„dividebothsidesby25}\\ x=2\end{array}$

Substitute $x=2$in $6x+y=15$and solve for $y:$

$\begin{array}{c}6x+y=15\\ 6\left(2\right)+y=15\text{ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„substitute2for}x\\ 12+y=15\text{ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„simplify}\\ y=3\text{ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„subtract12frombothsides}\end{array}$

So, the solution of the given system is $\left(x,y\right)=\left(2,3\right)$.