Greetings!
"Solve:[tex]2y = x + 2[/tex] and [tex]x - 3y = -5[/tex]?"...
Solve using substitution:
[tex]2y=x+2[/tex]
[tex]y=(x+2)/2[/tex]
----------------------------
[tex]x -3y = -5[/tex]
is also
[tex]x - 3((x+2)/2) = -5[/tex]
Solve for x.
[tex]x - 3((x+2)*1/2) = -5[/tex]
Distribute the parenthesis.
[tex]x - 3(x*1/2+2*1/2) = -5[/tex]
Simplify.
[tex]x - 3(1/2x+1) = -5[/tex]
Distribute the parenthesis.
[tex]x - (3*1/2x+3*1)= -5[/tex]
Simplify
[tex]x - (3/2x+3)= -5[/tex]
Add -3 to both sides.
[tex](x - (3/2x+3))+(-3)=(-5)+(-3)[/tex]
Simplify.
[tex]x - (3/2x)=-2[/tex]
Find LCM.
[tex]2/2x-(3/2x)=-2[/tex]
[tex]-1/2x=-2[/tex]
Multiply both sides by -2.
[tex](-1/2x)*(-2)=(-2)*(-2)[/tex]
Simplify.
[tex]x=4[/tex]
Now Input this constant in place of the variable x.
[tex]2y = x + 2[/tex]
[tex]2y = 4+2[/tex]
Add like terms.
[tex]2y = 6[/tex]
Divide both sides by 2.
[tex](2y)/2 = (6)/2[/tex]
Simplify.
[tex]y=3[/tex]
x=4 y=3
Hope this helps.
-Benjamin
