Question

Solve the system of linear equation 8X plus 5Y equals 18 and 6X plus Y equals -2 by using the linear Combination method Emmaus decided that he should first multiply the second equation by -5 and then add the two questions together to eliminate why terms is calculations are shown shown

Answer 1

$\text{The solution is } x = \frac{-14}{11} \text{ and } y = \frac{62}{11}$

Solution:

Given system of equations are:

8x + 5y = 18 ------- eqn 1

6x + y = -2 -------- eqn 2

Multiply eqn 2 by -5

-30x -5y = 10 ----- eqn 3

Add eqn 1 and eqn 3 so that y terms gets eliminated

8x + 5y = 18

-30x -5y = 10

( + ) --------------

-22x = 28

Divide both sides by -22

$x = \frac{28}{-22}\\\\x = \frac{-14}{11}$

Substitute the x value in eqn 1

$8(\frac{-14}{11}) + 5y = 18\\\\\frac{-112}{11} + 5y = 18\\\\5y = 18 + \frac{112}{11}\\\\5y = \frac{310}{11}\\\\y = \frac{62}{11}$

$\text{Thus the solution is } x = \frac{-14}{11} \text{ and } y = \frac{62}{11}$