Is (-5,-5) a solution to the system of equations: y = -2x - 15 y = 2x + 5
Understand the Problem
The question asks whether the point (-5, -5) is a solution to the given system of equations. To verify, we need to substitute x = -5 and y = -5 into both equations and check if they hold true. If both equations are satisfied, then the point is a solution to the system.
Answer
yes
Answer for screen readers
yes
Steps to Solve
- Substitute $x = -5$ and $y = -5$ into the first equation Replace $x$ and $y$ with $-5$ in the first equation $y = -2x - 15$.
$$ -5 = -2(-5) - 15 $$
- Simplify the first equation Simplify the right side of the equation.
$$ -5 = 10 - 15 $$ $$ -5 = -5 $$
The first equation is true.
- Substitute $x = -5$ and $y = -5$ into the second equation Replace $x$ and $y$ with $-5$ in the second equation $y = 2x + 5$.
$$ -5 = 2(-5) + 5 $$
- Simplify the second equation Simplify the right side of the equation.
$$ -5 = -10 + 5 $$ $$ -5 = -5 $$
The second equation is true.
- Determine if the point is a solution Since both equations are true when $x = -5$ and $y = -5$, the point $(-5, -5)$ is a solution to the system of equations.
yes
More Information
A solution to a system of equations is a set of values that satisfy all equations in the system simultaneously. In this case, the point (-5, -5) satisfies both equations, making it a solution to the system.
Tips
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