algebra
posted by Joel on .
Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
3x + 4y = 19.5
3x + y = 10.5

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