Is (8, 10) a solution to this system of equations? 19x - 14y = 12 11x - 10y = -12
Understand the Problem
The question asks whether the point (8, 10) is a solution to the given system of equations. To determine this, we need to substitute x = 8 and y = 10 into both equations and check if they hold true. If both equations are satisfied, then (8, 10) is a solution; otherwise, it is not.
Answer
Yes
Answer for screen readers
Yes
Steps to Solve
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Substitute $x = 8$ and $y = 10$ into the first equation We have the equation $19x - 14y = 12$. Substituting the values, we get: $19(8) - 14(10) = 152 - 140 = 12$. Since $12 = 12$, the first equation is satisfied.
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Substitute $x = 8$ and $y = 10$ into the second equation We have the equation $11x - 10y = -12$. Substituting the values, we get: $11(8) - 10(10) = 88 - 100 = -12$. Since $-12 = -12$, the second equation is satisfied.
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Determine if (8, 10) is a solution Since both equations are satisfied by $x = 8$ and $y = 10$, the point $(8, 10)$ is a solution to the system of equations.
Yes
More Information
A solution to a system of equations must satisfy all equations in the system.
Tips
A common mistake is making an arithmetic error when substituting and simplifying the expressions, especially with negative signs. Careful calculation is required. Another common mistake is to only test one of the equations.
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