Question

Solve the following equations graphically
x + y=3 & x-3y= -5

Answer 1

`(x,y)\rightarrow(1,2)`

Explanation:

Multiply first equation by 3 to help cancel out the "y" variable:

`\displaystyle \left \{ {{x+y=3} \atop {x-3y=-5}} \right.\\\\\rightarrow \left \{ {{3x+3y=9} \atop {x-3y=-5}} \right.`

Combine system of equations on both sides:

`(3x+3y)+(x-3y)=9+(-5)\\4x=9-5\\4x=4\\x=1`

Thus,

`x+y=3\\1+y=3\\y=2`