Solving Systems of Equations by Graphing
Solve the system by graphing
y= 2x+ 2
y=x
(-2,-2)
Use substitution to solve the system of equations.
y=–x+ 4
y= 3x
(1,3)
Use elimination to solve the system of equations.
x + y= 7
x − y=−3
(2,5)
Less than or equal to
Explain the line and shading
solid line with shading below
How do you find the solution to a system of linear inequalities?
Graph and find the shading overlap.
Solve the system by graphing.
18x− 3y= 21
y= 6x− 7
infinitely many solutions
Use substitution to solve the system of equations.
y= 2x– 10
2y=x– 8
(4,-2)
Use elimination to solve the system of equations.
x− 2y= 10
3x+y =−12
(-2,-6)
greater than
explain the line and the shading
dashed line with shading above
Graph the system of inequalities.
y ≤ 2x− 1
y >−x+ 3
True or False: (4,2) a solution?
True
Solve the system by graphing.
y= 6x+ 4
6x−y= 1
no solution
Use substitution to solve the system of equations.
x– 2y= 12
y= 3x+ 14
(-8,-10)
Use elimination to solve the system of equations.
6x+ 2y=−12
4x+ 3y= 7
(-5,9)
A line that separates the graph into regions.
boundary line
Graph the system of inequalities.
3x− 2y< 4
−2x− 6y <−12
True or False: (4,-2) a solution?
False
Use a graph to approximate the solution of the system.
y= 4x− 3
y= 8x− 5
(0.5, -1)
Use substitution to solve the system of equations.
y= 3x+ 8
2y= 6x+ 16
infinitely many solutions
Which solution method, graphing, substitution, or elimination, is the most appropriate for solving the system of equations?
6x −y= 16
x= 4y− 5
Substitution, since the second equation already expresses x in terms of y.
Graph
y≤ 3x−6
Slope:
Y-intercept:
boundary line:
Shading:
Slope: 3
Y-intercept: -6
boundary line: solid
shading: below
Graph the system of inequalities.
y< −x+ 4
y≥ 2x+ 4
True or False: (-2,6) a solution?
False
Caterer A charges $15 per person and $100 to set up tables. Caterer B charges $20 per person and $50 to set up tables. Graph a system of equations. For what number of guests will the cost of Caterer A be the same as the cost of Caterer B? What is the cost for that number of guests?
10 number of guests at a cost of $250.
A community theater sold a total of 400 full-price tickets for adults and children. The price was $8.00 per adult ticket and $5.00 per children’s ticket. If the total revenue was $2,750, how many adult tickets and how many children’s tickets were sold?
250 adult tickets and 150 children’s tickets
Determine whether the first system of equations is equivalent to the second system of equations. Explain.
3x+ 5y= 1
2x− 6y= 38
-----------
18x+ 30y= 6
10x− 30y= 190
Yes, the pair of systems is equivalent.
Each equation in the second system is the result of multiplying every number in one of the equations in the first system by a constant.
Graph
x− 2y>−4
Slope:
Y-intercept:
Boundary line:
Shading:
Slope: 1/2
Y-intercept: 2
Boundary line: dashed
Shading: below
Graph the system of inequalities.
2x+ 2y≥−6
x+y ≤−1
True or False:(-10,8) is a solution.
True