Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.

Question

-3x + 4y = -19.5
-3x + y = -10.5

Answer 1

-3x + 4y = -19.5
-3x + y = -10.5

-3x + y = -10.5
+3x +3x
y = 3x - 10.5

-3x +4y = -19.5

-3x +4(3x -10.5) = -19.5
-3x + 4(3x) + 4(-10.5) = -16.5

-3x +12x - 42 = -16.5

9x - 42 = -16.5
+42 = + 42
9x = 42 - 19.5

9x = 22.5

9x / 9x= 22.5 / 9
x = 2.5

Plug x into the original equation to solve for y
y = 3x - 10.5

y = 3(2.5) - 10.5
y = 7.5 - 10.5
y = -3

Solution: (2.5, -3)
Check
-3x + 4y = -19.5 -3x + y = -10.5
-3(2.5) + 4(-3) = - 19.5 -3(2.5) + -3 = -10.5
-7.5 + (-12) = -19.5 -7.5 + (-3) = -10.5
-19.5 = -19.5 -10.5 = -10.5
True True