Is (-3, -6) a solution to the following system of equations? 9x - 7y = 15 7x - 4y = -8
Understand the Problem
The question asks to check if the point (-3, -6) is a solution to the given system of linear equations: 9x - 7y = 15 and 7x - 4y = -8. To determine this, substitute x = -3 and y = -6 into both equations. If both equations are true for these values, then the point is a solution to the system.
Answer
No
Answer for screen readers
No
Steps to Solve
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Substitute into the first equation Substitute $x = -3$ and $y = -6$ into the first equation $9x - 7y = 15$: $$9(-3) - 7(-6) = 15$$
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Simplify the first equation Simplify the left side: $$-27 + 42 = 15$$ $$15 = 15$$ The first equation is true.
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Substitute into the second equation Substitute $x = -3$ and $y = -6$ into the second equation $7x - 4y = -8$: $$7(-3) - 4(-6) = -8$$
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Simplify the second equation Simplify the left side: $$-21 + 24 = -8$$ $$3 = -8$$ The second equation is false.
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Determine if the point is a solution Since the point must satisfy both equations to be a solution to the system, and the second equation is false, the point (-3, -6) is not a solution to the system.
No
More Information
A point is a solution to a system of equations if and only if it satisfies all equations in the system. In this case, the point (-3, -6) satisfies the first equation but not the second. Therefore, it is not a solution to the system.
Tips
A common mistake is to stop after checking only one equation. A point must satisfy every equation in the system to be a solution. Another common mistake is to make a mistake when substituting or simplifying the equations.
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