Step 1) Solve the second equation for xx:
3x = 5/4y + 23x=54y+2
color(red)(1/3) xx 3x = color(red)(1/3)(5/4y + 2)13×3x=13(54y+2)
color(red)(1/color(black)(cancel(color(red)(3)))) xx color(red)(cancel(color(black)(3)))x = (color(red)(1/3) xx 5/4y) + (color(red)(1/3) xx 2)
x = 5/12y + 2/3
Step 2) Substitute 5/12y + 2/3 for x in the first equation and solve for y:
12x - 5y = 8 becomes:
12(5/12y + 2/3) - 5y = 8
(12 xx 5/12y) + (12 xx 2/3) - 5y = 8
(color(red)(cancel(color(black)(12))) xx 5/color(red)(cancel(color(black)(12)))y) + (color(red)(cancel(color(black)(12)))4 xx 2/color(red)(cancel(color(black)(3)))) - 5y = 8
5y + 8 - 5y = 8
5y - 5y + 8 = 8
0 + 8 = 8
8 = 8
Because 8 does in fact equal 8 these two equations are parallel and the same. They have an infinite number of points the same.
