Is (-6, -8) a solution to this system of equations? 18x - 15y = 12 6x - 6y = 12
Understand the Problem
The question asks whether the point (-6, -8) is a solution to the given system of equations. To determine this, substitute x = -6 and y = -8 into both equations. If both equations are true, then the point is a solution. Otherwise, it is not.
Answer
Yes
Answer for screen readers
Yes
Steps to Solve
- Substitute x = -6 and y = -8 into the first equation
Substitute the values into $18x - 15y = 12$:
$18(-6) - 15(-8) = 12$
- Simplify the first equation
Calculate the values:
$-108 + 120 = 12$
$12 = 12$
The first equation is true.
- Substitute x = -6 and y = -8 into the second equation
Substitute the values into $6x - 6y = 12$:
$6(-6) - 6(-8) = 12$
- Simplify the second equation
Calculate the values:
$-36 + 48 = 12$
$12 = 12$
The second equation is also true.
- Determine if (-6, -8) is a solution
Since both equations are true when $x = -6$ and $y = -8$, the point $(-6, -8)$ is a solution to the system of equations.
Yes
More Information
A point is a solution to a system of equations if it satisfies all equations in the system. In this case, (-6, -8) satisfies both equations, making it a solution.
Tips
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