Graphing
When you solve a system of equations graphically, where can you find the solution on the graph?
The point of intersection of the 2 lines is the solution to the system.
3x + y = 9
If you were to replace x in the second equation, what could you substitute in its place?
2y + 7
If you were solving this system of equations using the elimination method, what would you do with the equations first?
2x + 7y = 14
4x - 7y = 6
Add the equations together to eliminate y
Would the graphed inequality have a solid or dashed boundary line?
3x < y - 14
dashed
The sum of two numbers is 104. Their difference is 68. What are the numbers?
What is the solution to the system of equations? (Use may use Desmos to graph)
y = 3x + 7
y = (-2/3)x - 4
(-3,-2)
What is always the first step in solving a system of equations with the substitution method?
Isolating a variable in one of the equations
What is always the first step in solving a system of equations using the elimination method?
Create a pair of additive inverses between one set of matching variables
(1/4)x > 3 - 2y
No
A shopper bought 6 shirts and 8 hats for $700. A week later, at the same prices, he bought 9 shirts and 6 hats for $660. What was the cost of one shirt?
$30
2x - 3y = 15
4x - 30 = 6y
There are infinite solutions to the system
Solve the system on scratch paper with the substitution method! (Desmos is not allowed)
-3x - 3y = 3
y = -5x - 17
(-4, 3)
Solve the system on scratch paper using the elimination method. (Desmos is not allowed)
-8x - 10y = 24
6x + 5y = 2
(7, -8)
Is (3, 5) included in the solution set of the system of inequalities?
2x + y > 8
1/4y < 1/4x + 2
YES
400 pre-ordered and 200 game-day
Rearrange the equation into slope-intercept form, so you can graph it on the coordinate plane.
3x=4y+20
y = (3/4)x - 5
2x + y = 20
6x - 5y = 12
(7, 6)
-9 + 5y = -4x
-11x = -20 + 9y
(1, 1)
How many solutions does the system of inequalities have?
y > (2/3)x + 1
y < (2/3)x - 3
zero
What are the dimensions of a rectangle whose perimeter is 78 inches, when the length of the rectangle is twice its width?
length: 26 inches and width: 13 inches
You find that a system of equations has no solutions. The first equation is:
y = (1/10)x - 11
What could the other equation be? Write an example
Anything in the form:
y = (1/10)x + b
(Same Slope, Different y-intercept)
Solve the system of equations on scratch paper using the substitution method. (Desmos is not allowed)
-3x + 3y = 4
-x + y = 3
no solution
Solve the system of equations on scratch paper using the elimination method. (Desmos is not allowed)
(-5/7) - (11/7)x = -y
2y = 7 + 5x
(-3, -4)
Write 3 points that would fall in the solution set of the system of inequalities:
3x + y > 2
y > (1/4)x - 2
answers will very (most fall in Quadrant I)
Anthony bought 6 video games and 2 used video games for $127.92. At the same prices, Mackenzie bought 3 new video games and 8 used video games for $133.89. What was the cost of a used video game?
$9.99