Is (5, 5) a solution to the system of equations y = -1/5x - 4 and y = 2x - 5?
Understand the Problem
The question asks whether the point (5, 5) is a solution to the given system of linear equations. To determine this, we will substitute x = 5 and y = 5 into each equation. If both equations are true, then (5, 5) is a solution; otherwise, it is not.
Answer
No
Answer for screen readers
No
Steps to Solve
- Substitute (5, 5) into the first equation
Substitute $x = 5$ and $y = 5$ into the equation $y = -\frac{1}{5}x - 4$: $$5 = -\frac{1}{5}(5) - 4$$
- Simplify the first equation
Simplify the right side: $$5 = -1 - 4$$ $$5 = -5$$
- Evaluate the first equation
Since $5 \ne -5$, the point (5, 5) is not a solution to the first equation.
- Substitute (5, 5) into the second equation
Substitute $x = 5$ and $y = 5$ into the equation $y = 2x - 5$: $$5 = 2(5) - 5$$
- Simplify the second equation
Simplify the right side: $$5 = 10 - 5$$ $$5 = 5$$
- Evaluate the second equation
Since $5 = 5$, the point (5, 5) is a solution to the second equation.
- Determine if (5, 5) is a solution to the system
For (5, 5) to be a solution to the system of equations, it must satisfy both equations. Since it only satisfies 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.
Tips
A common mistake is to stop after checking only one equation. It is important to check all equations in the system to confirm whether the point is a solution to the entire system.
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