7.1: Graphing Systems of Equations
State whether the systems of equations has
ONE SOLUTION, NO SOLUTION or INFINITE MANY
y=-3/2x + 5
y=-2/3x +5
One Solution
Use Substitution!!! to solve each system of equations
y = 5x + 1
4x + y = 10
(1,6)
Use ELIMINATION to solve each system of equations.
-x + y = 7
x + y = 1
(-3, 4)
Use elimination to solve each systems of equations
x + y = 2
-3x + 4y = 15
( 1 , -3 )
Solve each system of inequalities by graphing.
y<6
y>x+3
Indicate 2 points that would be included in the solution
Desmos--graph
(0,5)
(-1,3)
(there are many others)
What is the solution to the system of equations?
2x+y=4
3x+3y=12
(0, 4)
Use Substitution!!! to solve each system of equations
y = 3x + 4
-6x -2y = -8
(0, 4)
Use ELIMINATION to solve each system of equations.
-4x + 5y = 17
4x + 6y = -6
(-3 , 1 )
Use elimination to solve each systems of equations
2x + 5y = 11
4x + 3y = 1
( -2 , 3 )
Solve each system of inequalities by graphing.
y < x + 10
y > 6x + 2
Indicate 2 points that would be included in the solution.
Desmos-graph
Write the system of equations in slope intercept form?
-3x+y=6
2x+ y = 4
y=3x+6 & y=-2x+4
Use Substitution!!! to solve each system of equations
5x - y = 5
-x + 3y = 13
(2,5)
Use ELIMINATION to solve each system of equations.
a + 4b = -4
a + 10b = -16
( 4 , 2 )
Use elimination to solve each systems of equations
12x - 3y = -3
6x + y = 1
( 0 , 1 )
Solve each system of inequalities by graphing.
x + y < -1
x + y > 3
Indicate 2 points that would be included in the solution.
Desmos--graph
Write the system of equations in slope intercept form.
2x+y=5
4x +2y = 10
y=-2x+5
y=-2x+5
Use Substitution!!! to solve each system of equations
y = 3x + 2
2x + 2y = 20
(2 , 8)
2x + y = -8
x-y = 2
( -2 , -4 )
Mr. Santos, the curator of the children's museum, recently made two purchases of firing clay and poly clay for a visiting artist to sculpt. On Tuesday he bought 5 bogs of firing clay and 24 boxes of poly clay for $64.05. On Wednesday he bought 25 bags of firing clay and 8 boxes of poly clay for $51.45.
Create the systems of equations to represent this situation.
5x + 24y = 64.05
25x + 8y = 51.45
y < x + 2
y > x - 3
Solve the system of inequalities by graphing. Indicate 2 points that would be included in the solution.
Desmos-graph
Do PARELLEL LINES have one solution, no solution, or infinitely many?
no solution
Use Substitution!!! to solve each system of equations
y = -10x -2
-50x - 10y = 120
(2, -22)
Jeremy and Kendrick each bought snacks for their friends at a skating rink. Jeremy bought 4 bags of popcorn and 2 plates of nachos for $18.50. Kendrick bought 7 bags of popcorn and 2 plates of nachos for $26.75
Write the systems of equations.
4x + 2y = 18.50
7x + 2y = 26.75
2x + 3y = 13
x + y = 7
Solve the above system of equations
( 8 , -1 )
Graph the below system of inequalities
25x + 15y > 100
x + y < 6
desmos Graph