Problem: Solve using the elimination method. Show your work.
Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
10x + 5y = 52.5
30x – 7y = 80.5
1) 10x + 5y = 52.5
2) 30x – 7y = 80.5
Multiply equation 1 by 3.
3(10x + 5y) = 52.5 * 3
3) 30x + 15y = 157.5
Subtract equatioin 2 from equation 3.
30x + 15y = 157.5
-(30x – 7y = 80.5)
-------------------------
22y = 77
22y = 77
y = 77/22
y = 3.5
With that, use equation 1 to solve for x.
10x + 5y = 52.5
10x + 5(3.5) = 52.5
10x + 17.5 = 52.5
10x = 52.5 - 17.5
10x = 35
x = 35/10
x = 3.5
Check the values.
30x – 7y = 80.5
30(3.5) – 7(3.5) = 80.5
105 - 24.5 = 80.5
80.5 = 80.5
Answer: x = 3.5, y = 3.5