Find the solution of the system of equations: 9x + y = 28; 3x + 3y = -12.
Understand the Problem
The question is asking to find the solution to a system of linear equations. This involves solving for the variables x and y from the given equations.
Answer
The solution is \((4, -8)\).
Answer for screen readers
The solution to the system of equations is ((4, -8)).
Steps to Solve
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Write Down the Equations We have the following system of equations: [ 9x + y = 28 \quad (1) ] [ 3x + 3y = -12 \quad (2) ]
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Simplify the Second Equation We can simplify equation (2) by dividing all terms by 3: [ x + y = -4 \quad (3) ]
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Solve for y in the Second Equation From equation (3): [ y = -4 - x \quad (4) ]
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Substitute y into the First Equation Substitute equation (4) into equation (1): [ 9x + (-4 - x) = 28 ]
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Combine Like Terms Simplify the equation: [ 9x - x - 4 = 28 ] [ 8x - 4 = 28 ]
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Isolate x Add 4 to both sides: [ 8x = 32 ] Now divide by 8: [ x = 4 ]
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Substitute x Back to Find y Substitute (x = 4) into equation (4): [ y = -4 - 4 = -8 ]
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State the Solution The solution to the system of equations is: ( (x, y) = (4, -8) )
The solution to the system of equations is ((4, -8)).
More Information
In solving systems of linear equations, it is common to use substitution or elimination methods. Here, we simplified the second equation and substituted it back into the first equation to find the values of (x) and (y).
Tips
- Not Simplifying Correctly: Ensure to simplify equations properly before substituting.
- Sign Errors: Be cautious with negative signs when substituting values back.
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