Is (-2, -7) a solution to this system of equations? 10x - 5y = 15 3x - 8y = -50
Understand the Problem
The question is asking to verify if the point (-2, -7) is a solution to the given system of equations. We need to substitute x = -2 and y = -7 into both equations and check if the equations hold true.
Answer
No
Answer for screen readers
No
Steps to Solve
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Substitute x = -2 and y = -7 into the first equation Replace $x$ with $-2$ and $y$ with $-7$ in the equation $10x - 5y = 15$ $10(-2) - 5(-7) = 15$
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Simplify the first equation Multiply and simplify the equation from step 1. $-20 - (-35) = 15$ $-20 + 35 = 15$ $15 = 15$
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Substitute x = -2 and y = -7 into the second equation Replace $x$ with $-2$ and $y$ with $-7$ in the equation $3x - 8y = -50$ $3(-2) - 8(-7) = -50$
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Simplify the second equation Multiply and simplify the equation from step 3. $-6 - (-56) = -50$ $-6 + 56 = -50$ $50 = -50$
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Check if both equations are true The first equation, $10x - 5y = 15$, is true when $x = -2$ and $y = -7$ since we got $15 = 15$. The second equation, $3x - 8y = -50$, is false when $x = -2$ and $y = -7$ since we got $50 = -50$, which is not true Therefore, the point $(-2, -7)$ 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 (-2, -7) does not satisfy both equations, it is not a solution to the system.
Tips
A common mistake is to incorrectly perform the arithmetic when substituting and simplifying. Care should be taken with negative signs. Another common mistake is to assume that if it works for one equation, it automatically serves as a solution. All equations must be true for the given point!
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