Q. 70 - Intermediate Algebra

Question

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

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

Step-by-Step Solution

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 1 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 $3.$

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

Simplify parenthesis:

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

Multiply the second equation with $4$

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

Step 2 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 $y$

Consider:$5x+4 y =10$

Substitute:

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

Multiply:

$30+4 y =10$

$4y=-20$

$y=-20÷4$

$y=-5$

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