solve the linear equation by substitution.

Question

3x-6y=2

4x+3y=-1

Answer 1

3x - 6y = 2
4x + 3y = -1

 

Again, we need to find an easy way to isolate a variable. if we take a look at the first equation, we can see that both coefficients are multiples of three, so we can factor it out to give us a lone x:

3(x - 2y) = 2

x - 2y = 2/3

x = 2/3 + 2y

 

Now that we have a value for x, we can put that into the other equation"

4(2/3 + 2y)  + 3y = -1

8/3 + 8y + 3y = -1

8/3 + 11y = -3/3

11y = -11/3

y = -11/(3 * 11)

y = -1/3

 

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

x = 2/3 + 2(-1/3)

x = 2/3 - 2/3

x = 0

 

Let's check our answer:

3(0) - 6(-1/3) = 2

0 +2 = 2

2 = 2

4(0) + 3(-1/3) = -1

0 - 1 = -1

-1 = -1

Answer 2

3x-6y=2

4x+3y=-1

 

3x=2+6y

x=(2+6y)/3

 

(4)[(2+6y)/3]+3y=-1

(8+24y)/3+3y=-1

(8+24y)/3=-1-3y

8+24y=-3-9y

33y=-11

y=-1/3

 

x=[2+6(-1/3)]/3

x=[2+(-2)]/3

x=0