Question

Solve the system of equations by elimination and explain all your steps in words:

$\left\{\begin{array}{l}5x+4y=10\\ 2x=3y+27\end{array}\right.$

Short answer

The solution of system of system of linear equation $\left\{\begin{array}{l}5x+4y=10\\ 2x=3y+27\end{array}\right.$is $(6,-5)$

Step-by-step solution

Given information and creating variable with same coefficient

Given equations:

$$\begin{gathered} 5x+4y=10\dots ..\left(1\right) \\ 2x=3y+27\dots ..\left(2\right) \end{gathered}$$

Both equations are in standard form. So, elimination will work.

Multiply the first equation with $3.$

$3(5x+4y)=3\left(10\right)$

Simplify parenthesis:

localid="1658851619517" $15x+12y=30.....\left(3\right)$

Multiply the second equation with $4$

localid="1658851625849" $\begin{array}{c}4\left(2x\right)=4(3y+27)\\ 8x=12y+108\\ 8x-12y=108....\left(4\right)\end{array}$

solving for x and y

Solving equation $3$and $4$

Adding equations 3 and 4 we get

$x=138÷23$

$x=6$

Substitute $x=6$in any one of the equations and solve for localid="1658851682925" $y$

Consider:$5x+4y=10$

Substitute:

$5\left(6\right)+4y=10$

Multiply:

$30+4y=10$

$4y=-20$

$y=-20÷4$

$y=-5$

Hence the solution is$(6,-5)$