Answer:
We conclude that (4, 2) is NOT a solution to the system of equations.
Step-by-step explanation:
Given the system of equations
[tex]y = x - 2[/tex]
[tex]y = 3x + 4[/tex]
Important Tip:
- In order to determine whether (4, 2) is a solution to the system of equations or not, we need to solve the system of equations.
Let us solve the system of equations using the elimination method.
[tex]\begin{bmatrix}y=x-2\\ y=3x+4\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}y-x=-2\\ y-3x=4\end{bmatrix}[/tex]
Subtract the equations
[tex]y-3x=4[/tex]
[tex]-[/tex]
[tex]\underline{y-x=-2}[/tex]
[tex]-2x=6[/tex]
Now, solve -2x = 6 for x
[tex]-2x=6[/tex]
Divide both sides by -2
[tex]\frac{-2x}{-2}=\frac{6}{-2}[/tex]
Simplify
[tex]x=-3[/tex]
For y - x = -2 plug in x = -3
[tex]y-\left(-3\right)=-2[/tex]
[tex]y+3=-2[/tex]
Subtract 3 from both sides
[tex]y+3-3=-2-3[/tex]
Simplify
[tex]y=-5[/tex]
The solution to the system of equations is:
(x, y) = (-3, -5)
Checking the graph
From the graph, it is also clear that (4, 2) is NOT a solution to the system of equations because (-3, -5) is the only solution as we have found earlier.
Therefore, we conclude that (4, 2) is NOT a solution to the system of equations.
