Question

Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are added together, the y term is eliminated?

Answer 1

18 times the first equation and 8 times the second equation

Explanation:

we have

`(1)/(4)x-(1)/(6)y=5` ------> first equation

`(4)/(5)x+(3)/(8)y=10` ------> second equation

step 1

Multiply the second equation by 8 both sides to remove the fraction in the variable y

`8((4)/(5)x+(3)/(8)y)=10(8)`

`(32)/(5)x+3y=80`

step 2

Multiply the first equation by 18 both sides to obtain the coefficient -3 in the variable y

`18((1)/(4)x-(1)/(6)y)=5(18)`

`(18)/(4)x-3y=90`

step 3

Adds the new equation 1 and equation 2

`(18)/(4)x-3y=90\\\\ (32)/(5)x+3y=80\\ -------`

The y-term is eliminated

therefore

The answer is

18 times the first equation and 8 times the second equation