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? One-fourth x minus one-sixth y = 5 Four-fifths x + StartFraction 3 Over 8 y EndFraction = 10

Answer 1

The first equation must be multiplied by 18 and second equation must be multiplied by 8

Solution:

Given system of equations are:

$\frac{1}{4}x -\frac{1}{6}y = 5$ --------- eqn 1

$\frac{4}{5}x +\frac{3}{8}y = 10$ -------------- eqn 2

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

$8(\frac{4}{5}x +\frac{3}{8}y = 10)\\\\\frac{32x}{5} + 3y = 80 -------- eqn 3$

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

$18(\frac{1}{4}x -\frac{1}{6}y = 5)\\\\\frac{18}{4}x -3y = 90 ---------- eqn 4$

Add eqn 3 and eqn 4

$\frac{32}{5}x +3y +\frac{18}{4}x -3y = 80+90\\\\\frac{32}{5}x+\frac{18}{4}x = 170$

Thus the y-term is eliminated

Therefore, first equation must be multiplied by 18 and second equation must be multiplied by 8