Solve the system of equations: -9x - 2y = -12 and -3x = y.
Understand the Problem
The question involves solving a system of linear equations represented by two equations: -9x - 2y = -12 and -3x = y. The goal is to find the values of x and y.
Answer
The solution is \( (4, -12) \).
Answer for screen readers
The solution to the system of equations is ( (4, -12) ).
Steps to Solve
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Substitute the value of y Using the second equation, ( -3x = y ), we can substitute ( y ) in the first equation: $$ -9x - 2(-3x) = -12 $$
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Simplify the equation Now, simplify the equation: $$ -9x + 6x = -12 $$
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Combine like terms Combine the terms with ( x ): $$ -3x = -12 $$
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Solve for x Divide both sides by -3 to find ( x ): $$ x = 4 $$
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Find y using the value of x Now that we have ( x ), substitute it back into the second equation to find ( y ): $$ y = -3(4) = -12 $$
The solution to the system of equations is ( (4, -12) ).
More Information
The values ( x = 4 ) and ( y = -12 ) satisfy both equations in the system. You can check your work by substituting these values back into the original equations.
Tips
- Forgetting to substitute correctly into the first equation.
- Incorrectly combining like terms or making arithmetic mistakes while simplifying.
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