Solve the system of equations: 3x - 6y = 15 -2x + 4y = -10 What is the value of x and y?
- x = 0, y = -2.5
- x = 5, y = 0
- x = 10, y = 1
- x = -5, y = 0
Explanation
1) 3x - 6y = 15
2) -2x + 4y = -10
Step 1: Multiply equation (2) by 1.5 to align y coefficients with equation (1):
-2x + 4y = -10
× 1.5 →
-3x + 6y = -15
Step 2: Add equation (1) and the modified equation (2):
(3x - 6y) + (-3x + 6y) = 15 + (-15)
0 = 0
This means the two equations are dependent — they represent the same line.
Step 3: Express x in terms of y from equation (1):
3x - 6y = 15
3x = 15 + 6y
x = (15 + 6y) / 3 = 5 + 2y
Since infinitely many solutions exist, pick y = 0:
x = 5 + 2(0) = 5
y = 0
x = 5, y = 0
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