use the method of subtraction to solve the system of linear equations. 3x - y = 3 and 7x -2y = 10

Question

this should read 3x -y = 3

                        7x - 2y = 10

I am continually getting the methods confused, this is for algebra I

Answer 1

By subtracting you want to eliminate on of the variable so that you are only left with one. In this case it would be easier to get rid of the y.

so let multiply the top equation by two and you will get

6x - 2y = 6

7x - 2y = 10.        Subtract them

-x = -4

x = 4

then plug in the x to one of the equations and you can get your y, it is easier to plug into the first equation 

3x - y = 3

3(4) - y = 3

12 - y = 3 

y = 9

 

Answer 2

This is sometimes a difficult concept to grasp. What needs to be done is to eliminate one of the variables by subtracting the equations. So, what I am going to do is eliminate the y. How do we do that? One of the equations has to be modified. So, I am going to thake the first equation and multiply it by 2. So the new equation will be 6x-2y=6. Now, stack the equations like you are going to subtract them: 7x-2y=10 - 6x-2y=6 _____________ x=4 Then you solve for y by substituting into an original equation: 3(4) -y =3 12 -y =3 -y=-9 y=9 your solution set for the equations is the ordewred pair (4,9). If the lines were graphed, the point at (4,9) would be where the lines crossed. I hope this answers the question.