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

Answer:

18 times the first equation and 8 times the second equation

Step-by-step explanation:

we have

$\frac{1}{4}x-\frac{1}{6}y=5$ ------> first equation

$\frac{4}{5}x+\frac{3}{8}y=10$ ------> second equation

step 1

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

$8(\frac{4}{5}x+\frac{3}{8}y)=10(8)$

$\frac{32}{5}x+3y=80$

step 2

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

$18(\frac{1}{4}x-\frac{1}{6}y)=5(18)$

$\frac{18}{4}x-3y=90$

step 3

Adds the new equation 1 and equation 2

$\frac{18}{4}x-3y=90\\\\ \frac{32}{5}x+3y=80\\ -------$

The y-term is eliminated

therefore

The answer is

18 times the first equation and 8 times the second equation