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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

This week in math 10 we learned how to find the equations from the given slope and coordinates. We also learned how to find slopes on a graph using equations. There is 3 different types of equations, including slope Y intercept: This form can be written as y=mx+b where the mx is the slope and b is the y. General Form: This is found by taking an equation in Slope Y-intercept form and getting rid of any fractions while also moving the Y to the other side. The only way you can tell anything from is by turning it to a Slope Y intercept so you can graph it. And slope point form: Slope point form is the one of the easiest ways to write an equation of a line with. You can write it as m(xm-1m)=y-1

This week we learned about Slopes. The formula to find a slope is rise, which is the y-axis and run which is the x-axis. We also learned about the four different types of slopes positive, negative, zero, and undefined slope, to find these slopes, here are some helpful tips: slope = rise / run, rise is vertical on the Y axis, the run is horizontal on the X axis, positive slope is diagonal line going to the right, negative slope is diagonal line going to the left, zero slope is always horizontal, an undefined slope is always vertical and a nice point has no decimals in the slope.