Is (3, -4) a solution to the system of equations: y = -4x - 8 and y = -4?
Understand the Problem
The question asks whether the point (3, -4) is a solution to the given system of equations. To determine this, we need to substitute the values of x and y into both equations and check if the equations hold true. If both equations are true, then (3, -4) is a solution to the system.
Answer
No
Answer for screen readers
No
Steps to Solve
- Substitute $x$ and $y$ values into the first equation
Substitute $x = 3$ and $y = -4$ into the first equation $y = -4x - 8$.
- Evaluate the first equation
Evaluating the equation:
$y = -4x - 8$
$-4 = -4(3) - 8$
$-4 = -12 - 8$
$-4 = -20$
The first equation is NOT true.
- Substitute $x$ and $y$ values into the second equation
Substitute $y = -4$ into the second equation $y = -4$.
- Evaluate the second equation
Evaluating the second equation:
$y = -4$
$-4 = -4$
The second equation IS true.
- Determine if the point is a solution
Since the point (3, -4) does not satisfy both equations, 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. Since (3, -4) does not satisfy the first equation, it is not a solution to the system, even though it satisfies the second equation.
Tips
A common mistake is to only check one of the equations. Remember that for a point to be a solution to a system of equations, it must satisfy all equations in the system.
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