Solve the system of equations x, plus, y, equals, minus, 8x+y=−8 and minus, 3, x, minus, 4, y, equals, 34−3x−4y=34 by combining the equations.
Question
Solve the system of equations x, plus, y, equals, minus, 8x+y=−8 and minus, 3, x, minus, 4, y, equals, 34−3x−4y=34 by combining the equations.
Solution
To solve the system of equations:
- x + y = -8
- -3x - 4y = 34
We can use the method of combining the equations. Here are the steps:
Step 1: Multiply the first equation by 3 and the second equation by 1 to make the coefficients of x the same in both equations:
3*(x + y) = 3*(-8) -3x - 4y = 34
which gives us:
3x + 3y = -24 -3x - 4y = 34
Step 2: Add the two equations together:
(3x + 3y) + (-3x - 4y) = -24 + 34
which simplifies to:
-y = 10
Step 3: Multiply through by -1 to solve for y:
y = -10
Step 4: Substitute y = -10 into the first equation:
x + (-10) = -8
which simplifies to:
x = 2
So, the solution to the system of equations is x = 2, y = -10.
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