Question

18x-3y=-15
-6x+y=5
Solve by substitution

Answer 1

consistent system with equation
`y=6x+5`

Explanation:

`18x-3y=-15`,
`-6x+y=5`

To solve by substitution, we have to isolate a variable in one of the equations. I will isolate y in the second equation.

`-6x+y=5`

+6x +6x

`y=6x+5`

Next, substitute this y value for y in the first equation:

`18x-3y=-15`

`18x-3(6x+5)=-15`

and distribute.

`18x-18x-15=-15`

`-15=-15`

We are left with an equality of constants. This means that the system of equations is actually just one equation, meaning it has an infinite number of solvable points (this is sometimes called consistent). And, its equation is just what we solved for in the first step:

`y=6x+5`