Solve the system of equations 2, x, minus, 2, y, equals, minus, 42x−2y=−4 and minus, 4, x, minus, 3, y, equals, minus, 27−4x−3y=−27 by combining the equations.
Question
Solve the system of equations
Given the equations:
and
Combine the equations to solve the system.
Solution
Sure, let's solve the system of equations step by step.
The system of equations is:
- 2x - 2y = -4
- -4x - 3y = -27
First, let's simplify the first equation by dividing every term by 2:
x - y = -2
Now, we have:
- x - y = -2
- -4x - 3y = -27
Next, let's multiply the first equation by 4 to match the x term in the second equation:
4x - 4y = -8
Now, we have:
- 4x - 4y = -8
- -4x - 3y = -27
Now, let's add the two equations together:
4x - 4y + (-4x - 3y) = -8 - 27 -7y = -35
Divide by -7 to solve for y:
y = 5
Substitute y = 5 into the first equation:
x - 5 = -2 x = 3
So, the solution to the system of equations is x = 3 and y = 5.
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