Is (10, 8) a solution to this system of equations? 2x - 5y = -20 x + 9y = 14
Understand the Problem
The question asks to determine if the point (10, 8) is a solution to the given system of linear equations. This involves substituting x = 10 and y = 8 into both equations and checking if the equations hold true.
Answer
No
Answer for screen readers
No
Steps to Solve
- Substitute the given values into the first equation
Substitute $x = 10$ and $y = 8$ into the first equation $2x - 5y = -20$.
$2(10) - 5(8) = -20$
- Simplify the first equation
Simplify the equation obtained in the previous step.
$20 - 40 = -20$
$-20 = -20$
The first equation is true.
- Substitute the given values into the second equation
Substitute $x = 10$ and $y = 8$ into the second equation $x + 9y = 14$.
$10 + 9(8) = 14$
- Simplify the second equation
Simplify the equation obtained in the previous step.
$10 + 72 = 14$
$82 = 14$
The second equation is false.
- Conclusion
Since the point (10, 8) satisfies the first equation, but does not satisfy 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 simultaneously. Since the point (10, 8) does not satisfy the second equation, it is not a solution to the system.
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