Solve by Graphing
Solve the system of linear equations below using the graphing method.
x+y=0
x-y=0
(0,0)
Solve the system of linear equations below using the substitution method.
y+x=1
x=2y+4
(2,-1)
Solve the system of linear equations below using the elimination method.
y+2x=4
-y+x=2
(2,0)
What is a linear equation?
An equation with two variables that represents a straight line when plotted on a graph.
There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?
What is 6 chickens and 7 pigs?
Solve the system of linear equation below using the graphing method.
y=5x+8
1/5y=x+10
No solution
Solve the system of linear equations below using the substitution method.
y=2x+4
2x+y=8
(1,6)
Solve the system of linear equations below using the elimination method.
2y-x=4
4y+x=2
(-2,1)
A group of two or more linear equations.
Ex)
y=2x+4
2x+3y=8
Find the value of two numbers if their sum is 12 and their difference is 4.
What is (8,4) ?
Solve the system of linear equations below using the graphing method.
y=1/2x+8
2y=x+16
Infinite
Solve the system of linear equations below using the substitution method.
y=3x+4
3x=y-4
Infinite
Solve the system of linear equations below using the elimination method.
x-y=6
2x+2y=4
(4,-2)
What does it mean for a system of linear equations to have a solution?
If there is a solution, it is the intersection point of the lines.
John went to Yellow Stone National Park one day this summer. All of the people at the park were either hiking or bike riding. There were 178 more hikers than bike riders. If there were a total of 676 people at the park, how many were hiking and how many were riding their bikes?
427 hikers and 249 bikers
Solve the system of linear equations below using the graphing method (DESMOS).
y=2x+4
(-1/2)y=x+6
(-4,-4)
Solve the system of linear equations below using the substitution method.
y=8-x
-2x+-2y=4
No solution
Solve the system of linear equations below using the elimination method.
3x+2y=6
2x-3y=4
(2,0)
What is a coefficient?
Number attached to the variable
Ex) 2 in 2x, 3 in 3y
Harold had a summer lemonade stand where he sold small cups of lemonade for $1.25 and large cups for $2.50. If Harold sold a total of 155 cups of lemonade and collected a total of $265, how many cups of each type did he sell?
98 small cups and 57 large cups of lemonade
If the two linear equations represent parallel lines on the graph, how many solutions are there?
None
When would you use the substitution method over elimination?
When one of the linear equations is in slope-intercept form (y=mx+b).
When would you use the elimination method over the substitution method?
When the coefficients of the two linear equations are inverses of each other.
Ex) Below shows an example of the x variable having inverse coefficients.
-2x+y=6
2x+3y=8
Give me an example of coefficients that are inverses (opposites).
Answers vary.
Ex) 2y and -2y in the system of linear equations below.
2y-2x=4
-2y+x=5
Phil bought 6 new compact disks and 2 used compact disks for $127.92. At the same prices, Mackenzie bought 3 new compact disks and 8 used compact disks for $133.89. Find the cost of buying a single used compact disk.
$9.99