How do you solve algebraically the system of equations?

Answer 1

You can solve a system of equations using a few methods: elemination and subsitution.

In the elemination method you would multiply each of your equations by a factor that would cause one of the variables to be eleminated.

ex: If you had 2x-3y=5 and 3x+6y=4 you would multiply the first equation by a factor of 2 (distributing the 2 to each term), giving you a new equation of 4x-6y=10. Now your y terms would cancel. You line up the equations like:

3x+6y=4

4x-6y=10 you simply cancel the y terms and add the others giving you:

7x=14 you then solve for x (in this case divide by 7)

x=2

now you plug in x=2 into one of the first equations and solve

3x+6y=4

3(2)+6y=4 plug in x

6+6y=4 multiply

6y=-2 add like terms

y=-1/3 solve for y

To solve using the subsitution method you would take an equation and solve for one variable then plug that into the other equation.

ex. (using the same equations as before)

2x-3y=5

2x=3y+5

x=(3/2)y+(5/2)

3x+6y=4

3((3/2)y+(5/2))+6y=4 plug in for x

(9/2)y+(15/2)+6y=4 distribute the 3

(21/2)y=(-7/2) add like terms

y=(-1/3) solve for y

you would then plug in y and solve for x

2x-3(-1/3)=5

2x+1=5

2x=4

x=2

Hope this helps!