9th Grade Math, Unit 5

What is the graphing way to solve a system of linear equations?

A way to solve a system of equations by graphing via a graphing calculator and finding the point two lines intersect

What is the substitution method of solving linear equations?

For example, in the system of y=0.1x+3 and y=0.3x, you substitute y for 0.3x because y = 0.3x, and you substitute it in the original equation to create 0.3x=0.1x+3, you solve the equation to get x = 15, and you multiply x by 0.3 to get y = 4.5

What is the linear combination method?

A method of solving system of equations that involves multiplying the system so one variable becomes additive inverses that make 0 when added. For example if you have 5x+2y=10 and 2x+y=3 you multiply the second equation by -2 to get -4x-2y=-6 and you add both equations which cancels out the y value to create x=4. You then solve the equation normally.

How do you find the amount of solutions a system of eqautions has with the linear combination method?

If all variables cancel out and create a false statement, there are no solutions. But if all variables cancel out and there is a true statement like 0=0, there are infinitely many solutions. If there is just 1 solution for the variables, there is 1 solution.

How do you get rid of fractions?

By multiplying them with the multiplicative sum of their denominators. If you have 4/5 and 6/9, you multiply 4 and 9 and multiply both fractions with 36.

How do you graph 2 variable inequalities?

2 variable inequalities are first put into point slope form, and if there is a y > sign, the solution sets are shaded above the line. If there is a y < sign, the solution sets are shaded below the line. If the line is open and dotted, the solution sets are not included on the line. If the line is closed and filled, the solution sets in that area ARE included.
For example: Graphing y < -2x - 1., you write it as y=-2x - 1, graph the line (itll be dotted and open because its < > sign and not <= >= sign), and then you will shade below the line.

How do you graph 2 variable inequalities not in slope intercept form?

If the equation is not in slope intercept form like 2x - 2y <= 1, set y as 0 and find the x intercept and set x as 0 and find the y intercept and graph a line between the dots and shade accordingly. (you shade below the line, because the sign is not greater then or equal to for the y side.)

What does it mean if the shaded area in the line is below the line in a 2 variable inequality graph?

that y < mx + b

What does it mean if the shaded area is above the line in a 2 variable inequality graph?

That y is > mx+b

How to graph x <= 600?

x <= 600 is graphed as a solid line, and it is a vertical line because it is x. To test what side should be dashed you can replace the variable with a number on either side. In this case if you choose 6, 6 is less then 600 so you should graph the left side with 6 in it.