Answer:
The solution to the system of equations be:
Step-by-step explanation:
Given the system of equations
[tex]x-2y = 10[/tex]
x + 3y = 5
Solving the system of equations using the elimination method
[tex]\begin{bmatrix}x-2y=10\\ x+3y=5\end{bmatrix}[/tex]
subtracting the equations
[tex]x+3y=5[/tex]
[tex]-[/tex]
[tex]\underline{x-2y=10}[/tex]
[tex]5y=-5[/tex]
solving 5y = -5 for y
[tex]5y=-5[/tex]
Divide both sides by 5
[tex]\frac{5y}{5}=\frac{-5}{5}[/tex]
Simplify
[tex]y=-1[/tex]
For x - 2y = 10 plug in y = -1
[tex]x-2\left(-1\right)=10[/tex]
Apply rule -a(-a) = a
[tex]x+2\cdot \:1=10[/tex]
Multiply the numbers: [tex]2\cdot \:1=2[/tex]
[tex]x+2=10[/tex]
subtract 2 from both sides
[tex]x+2-2=10-2[/tex]
Simplify
[tex]x=8[/tex]
Therefore, the solution to the system of equations be:
The graph of the solution to the system of equations is also attached below.
