Answer:
[tex]x = 4[/tex]
[tex]y = 4[/tex]
Step-by-step explanation:
Given
[tex]3y = \frac{3}{2}x + 6[/tex]
[tex]y-\frac{1}{4}x = 3[/tex]
Required
The solution
Multiply the second equation by 3
[tex]3 * [y-\frac{1}{4}x = 3][/tex]
[tex]3y-\frac{3}{4}x = 9[/tex]
Rewrite as:
[tex]3y =\frac{3}{4}x + 9[/tex]
Subtract this from the first equation
[tex][3y = \frac{3}{2}x + 6]- [3y =\frac{3}{4}x + 9][/tex]
[tex]3y - 3y = \frac{3}{2}x - \frac{3}{4}x + 6 - 9[/tex]
[tex]0 = \frac{3}{4}x -3[/tex]
Rewrite as:
[tex]\frac{3}{4}x =3[/tex]
Multiply both sides by 3/4
[tex]x =3*\frac{4}{3}[/tex]
[tex]x = 4[/tex]
Substitute [tex]x = 4[/tex] in [tex]3y = \frac{3}{2}x + 6[/tex]
[tex]3y = \frac{3}{2} * 4 + 6[/tex]
[tex]3y = 6 + 6[/tex]
[tex]3y = 12[/tex]
Divide both sides by 3
[tex]y = 4[/tex]
