1) x/2 - (2y)/3 = 12
Transform to equation of the line in standard form ax + by = c
LCD: (2) (3)
(3)(2)x - (2)(3)(2y) = 12 (2)(3)
2 4
3x - 4y = 72, Equation 1
2) x/5 + 2y = 4
Transform to equation of the line in standard form:
LCD: 5
5x + (5) (2y) = (5)(4)
5
x + 10y = 20
x = -10y + 20, Equation 2
3) Substitute - 10y + 20 in Equation to for x in Equation 1.
3(-10y + 20) - 4y = 72
-30y + 60 - 4y = 72
-30y - 4y = 72 - 60
-34y = 12
-34y = 12
- 34 -34
y = -12/34 or -6/17
y = -6/17
4) Subsitute -6/17 for y in Equation 2 (x = -10y + 20)
x = -10 (-6/17) + 20
x = 60/17 + 20
LCD: 17
x = 60 + 340
17 17
x = 400/17
x = 400/17 y = -6/17
To check:
x/2 - (2y)/2 = 12
400/17 - 2 (-6/17) = 12
2 3
(400/17) (1/2) - (-12/17)(1/3) = 12
400/34 + 4/17 = 12
200/17 + 4/17 = 12
204/17 = 12
12 = 12
x/5 + 2y = 4
400/17 + 2(-6/17) = 4
5
(400/17) (1/5) - 12/17) = 4
80/17 - 12/17 = 4
68/17 = 4
4 = 4