Solve by substitution

Question

3x-6y=5

2y=4x-6

Answer 1

Multiply the second equation by 3.

 

2y = 4x - 6   ---->   6y = 12x - 18

 

 

Substitute this value of 6y into the first equation.

 

3x - (12x - 18) = 5

 

 

Solve for x from this equation.

Answer 2

LOOK AT YOUR SECOND EQUATION: when it's divided by two it says y = 2x - 3.

Then substitute this (for y) in the first equation.  EASY, right?

Answer 3

Hi Mackenzie,

 

Let's keep the equations the same and look at whatever relationship they have.

 

3x - 6y = 5     and 2y = 4x - 6

 

Notice how there's 6y in the first equation and in the second, 2y? We can multiply the second equation by 3 to get 6y.

 

So let's multiply 2y by 3 and similarly, what 2y is equal to by 3:

 

2y = 4x - 6   →   6y = 12x - 18

 

Plugging this new equation into our first:

 

3x - (12x - 18) = 5

 

We can now solve for x:

 

3x - 12x + 18 = 5

 

-9x = -13

 

x = 13 / 9

 

To find y, we can use any equation that we are given. In this case, I will use the first one still.

 

3 (13 / 9) - 6y = 5     (Now we are solving for y.)

 

13 / 3 - 6y = 5

 

-6y = 2 / 3

 

y = -2 / 18 or -1 / 9

 

Hope this helps!