how do i solve a substitution problem if in both equations y is in the second place

Question

the problem i am stuck on is -3x+7y=13 and 3x-4y=-1

Answer 1

Hi, Eric.

To solve a problem using substitution, you just need to solve one of the equations for one variable and then substitute it into the 2nd equation.

-3x + 7y = 13

3x - 4y = -1

This is an easy equation to solve for since the first equation has 3x as a term. Therefore, let's solve for 3x with the 1st equation:

-3x + 7y = 13

add 3x to both sides:

-3x + 3x + 7y = 13 + 3x

7y = 13 + 3x

Now subtract 13 from both sides:

7y - 13 = 13 - 13 + 3x

7y - 13 = 3x

Now you have an equation for 3x. Simply substitute it into the 2nd equation:

3x - 4y = -1

(7y - 13) - 4y = -1

3y - 13 = -1

Now, add 13 to both sides to isolate the 3y.

3y - 13 + 13 = -1 + 13

3y = 12

y = 12/3 = 4

Now. you can substitute 4 into either of the equations to find the value of x.

3x - 4(4) = -1

3x - 16 = -1

add 16 to both sides:

3x = 15

x = 5

Therefore ,

x = 5

y = 4

If these answers are correct, you should be able to substitute them into both of the equations to check your answers.

-3(5) + 7(4) = 13

-15 + 28 = 13 This solution works for this equation.

3(5) - 4(4) = 15 - 16 = -1 The solution is also correct for the 2nd equation.

Therefore,

x = 5

y = 4