May 2019 archive

Week 14 – Math 10

This week in Math 10 we learned about Systems of linear equations.

3 different types of linear equations

– No solutions

– One solution

– Infinite Solutions

 

 

First – what is a solution of a linear equation? we can graph all proper linear equations and if we have an equation of y=3x+4 and y=2x+3

The solution – these two equations is the points where both of the lines when graphed touch when graphed.

No Solution – when graphed the lines would be parallel. two parallel lines never touch. You can also tell if two equations have no solution if you only look at the written equation. For example if both equations have the same slope and the y-intercepts are different, this means the equation will have no equation.

y=5x+2

y=5x+5

^ no solution. If you were to put these two equations into demos, you would end up with two parallel lines.

One Solution – when a linear equation has one solution that means when graphed, somewhere along the graph the two lines will cross, sort of like an X shape. Now when written out, if both linear equations have different slopes than that means they will cross at one point. Even if the y-intercepts are the same it doesn’t matter, only the slopes need to be different.

y=6x+3

y=8x+2

These two equations are will have at least one solution guaranteed.

Infinite Solutions – So a linear equation with infinite solutions means that when graphed, the two lines will be on top of each other. If written, you can tell two equations will have infinite solutions if the slopes are the same and the y-intercepts are the same.

y=4x+3

4x-y=-3

These two equations will have infinite solutions since they are on top of each other

Week 15 – Math 10

this week in math 10 – we learned about the method of substitution.

substitution is the algebraic method of finding a solution for a system.

when doing the method of substitution – remember BFSD

B- brackets àexpand

F – Fraction àeliminate fractions

S – Sorting àorganize the numbers and like terms.

D – Divideànumber infant of Y

example:

x + 3y = 19 àrearrange àx = -3y +19

–> 4x- 2y à4(-3y +19) -2y = -12y + 76

= -10y +76

-10     -10

 

Y = 66

 

 

NOW USE Y TO SOLVE FOR X

X + 3y = 19 àx + 3(66) =19

 

3 x 66 = 198 + x = 19

 

X= -179

 

Week #13 – Math 10

WEEK 13 – point slope form

 

This week in math 10 we learned about point slope form. Usually to find the slope formula you use the equation of

m= y1-y2/x1-x2 BUT to find point slope form you switch/move the equation to

m(x1-x2) = y1-y2

a good way to remember what you’re doing in point-slope form is to remember to ‘plug + play’.

That basically means to plug in the numbers into the equation and let algebra take over! Easy!

week #12 – Math 10

WEEK 12- slope formula

This week in math 10, we learned about slope formula. Slope formula is equal to

change y/change x

and that is equal to

y1-y2/x1-x2

 

Example: (3,7) and (-2,11)

 

Also keep in mind that 5/-4 would be equal to -4/5 ,  it all depends on how you do your equation