Is (4, 9) a solution to the system of equations: y = 3x - 2, x = 4?
Understand the Problem
The question asks whether the point (4, 9) is a solution to the given system of equations. To determine this, we will substitute x = 4 and y = 9 into the equation y = 3x - 2 and check if the equation holds true, and also check that x = 4.
Answer
No
Answer for screen readers
No
Steps to Solve
- Substitute x = 4 into the first equation
We need to check if the point (4, 9) satisfies the equation $y = 3x - 2$. We substitute $x = 4$ into this equation
$y = 3(4) - 2$
- Simplify the equation to find y
Now, calculate the value of $y$:
$y = 12 - 2$ $y = 10$
- Check if the calculated y matches the given y
The calculated value of $y$ is 10, but the given point has $y = 9$. Therefore, the point (4, 9) does not satisfy the equation $y = 3x - 2$. The point must satisfy BOTH equations to be a solution
- x Check
Since the point (4, 9) has $x = 4$, it satisfies the second equation $x = 4$.
- Final Check
However, since the point (4, 9) 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. In this case, the point (4, 9) satisfies $x=4$ but not $y=3x-2$, so it not a solution to the system.
Tips
A common mistake is to only check one of the equations in the system. To be a solution, the point must satisfy all equations.
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