Is (-6, 6) a solution to this system of equations? 17x + 15y = -12, 8x + 5y = -3
Understand the Problem
The question asks whether the point (-6, 6) is a solution to the given system of linear equations. To determine this, substitute x = -6 and y = 6 into both equations. If both equations are true, then the point is a solution.
Answer
no
Answer for screen readers
no
Steps to Solve
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Substitute $x = -6$ and $y = 6$ into the first equation We have $17x + 15y = -12$. Substituting the values, we get $17(-6) + 15(6)$.
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Simplify the first equation $17(-6) = -102$ and $15(6) = 90$. Therefore, the left side of the equation becomes $-102 + 90 = -12$.
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Check if the first equation is satisfied Since $-12 = -12$, the first equation is satisfied.
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Substitute $x = -6$ and $y = 6$ into the second equation We have $8x + 5y = -3$. Substituting the values, we get $8(-6) + 5(6)$.
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Simplify the second equation $8(-6) = -48$ and $5(6) = 30$. Therefore, the left side of the equation becomes $-48 + 30 = -18$.
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Check if the second equation is satisfied Since $-18 \ne -3$, the second equation is not satisfied.
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Determine if the point is a solution Since the point $(-6, 6)$ satisfies the first equation but not the second equation, it is not a solution to the system of equations.
no
More Information
A solution to a system of equations must satisfy all equations in the system. Since $(-6, 6)$ does not satisfy both equations, it is not a solution to the system.
Tips
A common mistake is to only check one of the equations. A point must satisfy all equations in the system to be a solution. Another mistake is to make arithmetic errors when substituting and simplifying.
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