Solutions
a. 2x + 3y = 5
x - 5y = 9 -----> x = 5y + 9
2(5y + 9) + 3y = 5
10y + 18 + 3y = 5
13y + 18 = 5
13y = -13
y = -1
x = 5y + 9
x= 5(-1) + 9
x = 4
Final Answer: (4, -1)
b. -x + 2y = 3 -----> -x = -2y + 3
4x -5y = -3
4(2y - 3) -5y = -3
8y - 12 - 5y = -3
3y - 12 = -3
3y = 9
y = 3
-x = -2y + 3
-x = -2(3) + 3
-x = -6 + 3
-x = -3
x = 3
Final Answer: (3,3)
c. 6x + 4y = 20
3x + y = 5 ------> y = -3x + 5
6x + 4y = 20
6x + 4(-3x + 5) = 5
6x - 12x + 20 = 5
-6x + 20 = 5
-6x = -15
x = 15/6
y = -3x + 5
y = -3(15/6) + 5
y = -12.5
Final Answer: (15/6, -12.5)
d. 7x + 8y = 12
2x + y = 15 -----> y =-2x + 15
7x + 8(-2x+15) = 12
7x - 16x + 120 = 12
-9x = -108
x = 12
y = -2x + 15
y = -2(12) + 15
y = -24 + 15
y = -9
Final Answer: (12, -9)
e. x + 2y = 2 -----> x = -2y + 2
4x - 5y = -3
4(-2x + 2) -5y = -3
-8x + 8 - 5y = -3
-13x + 8 = -3
-13x = -11
x = 11/13
x = -2y + 2
-11/13 = -2y + 2
2.8 = -2y
y = -1.4
Final Answer: (11/13, 1.4)