solve the system by substitution

Question

solve  the system by substitution X=y-6
3x+2y=2

Answer 1

Substitution means we replace a variable with a known value:

x = y - 6

3x + 2y = 2

 

We have a value for x, so we put that into our equation:

3(y - 6) + 2y = 2

 

Now we just need to isolate y. We'll start by distributing that 3:

3y - 18 + 2y = 2

Combine like terms:

5y - 18 = 2

Move the constants to one side:

5y - 18 + 18 = 2 + 18

5y = 20

Now isolate y by dividing both sides by 5:

5y / 5 = 20 / 5

y = 4

 

Now that we know y, we can solve for x:

x = 4 - 6

x = -2

 

Now to check our answers:

3 * -2 + 2 * 4 = 2

-6 + 8 = 2

2 = 2