Systems Of Linear Equations Solving linear equations by graphing, substitution, and elimination Solving linear equations by graphing, substitution, and elimination. Solving linear equations by graphing, substitution, and elimination Graphing Substitution Elimination Use slope-intercept form y=mx+b When two lines intercect,

the coordinance of the intersection will be

the solution for the X and Y variables,

solving the equation. y-intercept slope When two equations are graphed to

form the same line, there will be infinitely

many solutions to the system. When two lines run parallel to each other,

there will be no solution for the system. There will be two different equations when you use this method;

each with two different variables that need to be solved for. It will

be easiest to solve for the variable with the coefficient of one; also

try to avoid fractions. For example: y=x-7 and 2x+y=8 Here, I'll substitute x-7 for y in the opposite equation. For example: 2x+x-7=8 Now, I'll finish out the equation by adding or subtracting like terms. For example: 3x-7=8

+7 +7

3x=15

Lastly, 3 divided by 15 will give you the solution of 5. After you have solved your first variable, you will plug it into the equations

and see if it equals the same number for both problems. If it does, you've got

the correct solution. For example: 5-7=-2

2(5)-2=8

Your solution is (5,-2) With this method, there will also be two equations, and both will have two pairs of variables (sometimes with coeffecients) that are opposite. this means they will cancel each other out and can be eliminated from the equations. For example: x+2y=7 and

3x-2y=-3 In this equation, the 2y variable and coeffecients are opposite;

one negative and the other positive. After these have been eliminated, add up the the remaining coeffecients, variables, and the numbers on the other side of the equal sign. For example: x+3x and 7+(-3) =

4x=4 Lastly, you would divide the coeffecient by the number on the other side of the equal sign to get the variable alone. From there, you have that variable's solution, plug it into both equations, and see if you get the same answer for both problems. For example: 4 divided by 4 = 1

x=1

1+2(3)=7 and 3(1)-2(3)=-3

Your solution would then be (1,3) WARNING! Some variables are going to need a coeffecient because they don't already have one. Some

might also need to be changed from positive to negative to be opposites. For example: 7x+3y=25 and

-2x-y=-8 It would be easiest to change the equation that has a variable by itself. That way, you can

multiply it to be the opposite of the coeffecient with the same variable. For example: 3(-2x-y=-8) (Be sure to distribute to ALL the numbers within the parentheses) 7x+3y=25

-6x-3y=-24 From here, you would finish off the equation normally and find the solution to be

(1,6) Let's see if you learned something. Adult tickets to a play cost $5 and student tickets cost $3.

In all 90 tickets were sold for a total of $334. How many

adult tickets were sold?

* Use any method to solve the problem Your first equation should look like: x+y=90

Your second equation should look like: 5x+3y=334 Using any method, your answer should be adult 32 tickets Now you know how to solve systems. Thanks for watching! Rise over run

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# Systems Of Linear Equations

solving linear equations through graphing, subtitution, and elemination.

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