Answer:
The point (4,7) is a solution to the system of equations.
Please also check the attached graph.
Step-by-step explanation:
Given the system of equations
[tex]y=2x-1[/tex]
[tex]y=\frac{1}{2}x+5[/tex]
Let us solve the system of equations using the elimination method
[tex]\begin{bmatrix}y=2x-1\\ y=\frac{1}{2}x+5\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}y-2x=-1\\ y-\frac{1}{2}x=5\end{bmatrix}[/tex]
subtracting the equations
[tex]y-\frac{1}{2}x=5[/tex]
[tex]-[/tex]
[tex]\underline{y-2x=-1}[/tex]
[tex]\frac{3}{2}x=6[/tex]
now solving [tex]\frac{3}{2}x=6[/tex] for x
[tex]\frac{3}{2}x=6[/tex]
Multiply both sides by 2
[tex]2\cdot \frac{3}{2}x=6\cdot \:2[/tex]
Simplify
[tex]3x=12[/tex]
Divide both sides by 3
[tex]\frac{3x}{3}=\frac{12}{3}[/tex]
Simplify
[tex]x=4[/tex]
For [tex]y-2x=-1[/tex] plug in x = 4
[tex]y-2\cdot \:4=-1[/tex]
[tex]y-8=-1[/tex]
Add 8 to both sides
[tex]y-8+8=-1+8[/tex]
Simplify
[tex]y=7[/tex]
Therefore, the solution to the system of equations is:
(x, y) = (4, 7)
Hence, the point (4,7) is a solution to the system of equations.
Please also check the attached graph.
