Answer:
[tex](2, 4)\rightarrow\text{First system}[/tex]
[tex](4, -2)\rightarrow\text{Second system}[/tex]
Step-by-step explanation:
First system:
We can substitute 2x for y:
[tex]6x-y=8\\6x-2x=8\\4x=8[/tex]
Divide both sides by 4
[tex]x=2[/tex]
Substitute 2 for x to solve for y:
[tex]y=2x=2(2)=4[/tex]
[tex](x, y)=(2, 4)[/tex]
Second system:
We can isolate x in the second equation by subtracting 4y from both sides:
[tex]x=-4-4y[/tex]
Now, substitute this value for x in the first equation:
[tex]3(-4-4y)+5y=2\\[/tex]
Distribute the 3 to each term in the parentheses:
[tex]3(-4)+3(-4y)+5y=2\\-12-12y+5y=2\\-12-7y=2[/tex]
Add 12 to both sides:
[tex]-7y=14[/tex]
Divide both sides by -7
[tex]y=-2[/tex]
Now, substitute -2 for y to solve for x:
[tex]x=-4-4y=-4-4(-2)=-4+8=4[/tex]
[tex](x, y)=(4, -2)[/tex]
