This week in math 10 new learned about systems of linear equations. A system of equations is a set of equations that you use all together at once. For example:

4x-y-22=0

2x+2y=6

So you start of by isolating the X or the Y from ether equation

4x-y-22+0 –> 4x-22=y

2x+2y=6 (this stays the same)

then you put the 4x-22 toward where ever a Y is on the other equation

2x+2(4x-22)=6

then you distribute the 2 into the 4x-22

2x+8x-44=6

now you collect like terms and put -44 on the side with the =6 but adding 44 to both sides

10x=50

now you divide and you find x

x=5

To find y, you just need to put the x=5 back into the equation

4(5)-y-22=0 –> 20-y-22=0

isolate the y

y=-2

OR

you can you elimination

4x+2y=6

3x=2y=8

add or subtract the two equations, we want to get two of the terms to cancel out

so in this equation we already have +2y and a -2y so they already cancel out when adding

so when adding we turn out with

7x=14

Divide

x=2

To find y, you once again have to put the x=2 back into one of the equations

4(2)+2y=6 –> 8+2y=6 –> 2y=-2

y=-1