Week 17 Math 10
Systems:
This week we started on our last chapter in math 10, systems of linear equations. We learned about the 3 different ways to solve these equations. The 3 ways are, graphing, substitution, and elimination, my favourite being elimination.
Graphing example:
- Always make both given equations into slope y-intercept form (y=mx+b)
- m= slope & b= y intercept
- only use this when you have small and simple numbers (no fractions or decimals as the y intercept because they can be hard to graph)
- graph both lines with the 2 bits of information (slope and y-intercept)
- find the spot where the 2 lines intersect and find its coordinates (this is your answer)
Substitution example:
- It doesn’t matter what variable you iscolate first
- To get the second variable (x or y) substitute the number you got on the previous step into the x or y place and solve again
- ALWAYS check your answers by putting the coordinates back into both equations and solving to see if the equation works
- Need to know BEDMAS and algebra to solve
Elimination example:
- your goal is to make a zero pair with one of the 2 variables (doesn’t matter what one)
- zero pair= when 2 numbers add to zero so they just cancel out and disappear
- to make a zero pair you need one positive and one negative of the same number and variable
- like in substitution when you have solved for one variable put in back into the equation to solve for the other
- example of zero pair= -2x & 2x
- if there arnt already any zero pairs you can make one by multiplying an entire equation by the same number
- after cancelling out a zero pair add the 2 equations together
- after adding and finding the first variable solve for the other variable by inputing the x or y into the other equation
- ALWAYS CHECK your answer by inputing both variables into their places and solving