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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.

This week we reviewed Functions and relations from grade 9. Functions are types of relation with only 1 connection with another number or variable or basically a special relation ship that you only have 1 of, like your spouse. We also learned about function notation. Function notation is a way a function is written and it is a different way then using the both X and Y in an equation. It is meant to be a way of giving information about the function without being a very long equation or explanation. The functions are usually a single letter like F or G or basically any letter.

Examples:

So this week in math we had our math mid term and since we just did review, we where asked to make an informative video from our previous units. So I did trigonometry because I found that to be an easy unit.

This week in Math 10 we finished off the polynomials and factoring unit. During this week we learned how to factor factor perfect trinomials in preparation for the unit test.

Here are some helpful hints on factoring perfect square trinomials: don’t for get to use CDPEU (Common factors, difference in squares, pattern, easy and ugly), The first and last terms are always perfect squares and the middle term is the root of the first and last term x 2.