Question

Solve the system of linear equations by substitution. y=2x+5 and y=3x-1

Answer 1

Plug in the second equation into the first equation for y.

`y = 2x + 5 \\ y = 3x - 1 \\ 3x - 1 = 2x + 5`
Now put the variable on one side and constants on the other

`3x - 1 + 1 - 2x = 2x - 2x + 5 + 1 \\ x = 6`
Now plug that back into one of the original equations

`y = 2x + 5 \\ y = 2(6) + 5 \\ y = 12 + 5 \\ y = 17`
So now you know

`x = 6 \\ y = 17`
Its always a good idea to check

`17 = 2(6) + 5 \\ 17 = 17 \\ 17 = 3(6) - 1 \\ 17 = 17`