Solving Systems by Graphing
How do you determine the solution to a system of equations by graphing?
Find the point where the two lines intersect.
What are the steps for solving a system of equations using elimination method?
Make sure equations are lined up.
Get common coefficients if there aren't any.
Add or subtract the equations to eliminate the variable with common coefficients.
Solve for the remaining variable.
Plug in your answer and solve for the other variable.
What are the steps to solve a system of equations using substitution?
Solve one equation for x or y.
Substitute it into the other equation and solve.
Plug your answer back in and solve for the other variable.
What is the difference between solutions for systems of linear equations and systems of linear inequalities?
Systems of linear equations have one solution (unless no solution or infinite solutions). Systems of inequalities have many solutions.
It is important to include what with your answers for word problems?
Units! (or labels)
What does it mean if the system has no solution?
The lines are parallel.
How would you set up these equations to use elimination method?
7x+5y=-13
-2x=7y+26
Line them up then multiply for common coefficients:
2(7x+5y=-13) 14x+10y=-26
7(-2x-7y=26) -14x-49y=182
Do graphing method and substitution method give you the same solution for the system of equations?
YES! Both will give you the point that makes both equations true.
When do you use a dotted line and when do you use a solid line when graphing inequalities?
Dotted: > or <
Solid: > or <
If we defined x as pants and y as shirts when solving a word problem, then determined the point (3,3) was in the solution area, how would you interpret that answer?
3 pants and 3 shirts
What does it mean if the solution is infinite?
It is the same line.
How do you find common coefficients?
Multiply the whole equation
Set up the following system of equations for substitution method:
x+4y=0
3x+2y=20
x=-4y
3x+2y=20
3(-4y)+2y=20
When do you shade above the line and when do you shade below?
Above: > or >
Below: < or <
Give the equations for the following word problem:
Mary knits scarves and sweaters to sell. Scarves take 2 hours to knit and sweaters take 10 hours. Mary would like to spend no more than 40 hours per week knitting at knit at least 5 items per week.
2x+10y < 40
x+y > 5
Name the three steps to solve a system of equations by graphing.
1.) Put the equations in slope-intercept form.
2.) Graph the lines.
3.) Identify the solution - the point where the lines intersect.
When do you add and when do you subtract?
Add: When you have opposite signs for the common coefficients
Subtract: When sign are the same for the common coefficients
Is (-9,5) the correct solution for the system of equations:
x-3y=-24
5x+8y=-5
Yes! (-9,5) makes both equations true.
-9-3(5)=-24
-9-15=-24
5(-9)+8(5)=-5
-45+40=-5
How do you determine the solutions for a system of linear inequalities?
Where the shaded regions overlap on the graph
Bob bought 24 hockey tickets for $83. Adult tickets cost $5.50 and child tickets cost $2.00. How many child tickets did he buy?
14 child tickets
Draw a graph to show the solution for the system:
y= -x + 3
y= x - 1
(2,1)
Solve the system using elimination:
2x - 6y =12
-5x+15y=-30
Infinite!
0=0
Free Points
Enjoy
Which ordered pairs make the linear inequality true:
5x - y > 4
a.) (4,2)
b.) (-3,1)
c.) (8,4)
d.) (2,7)
A and C
Give the equations for the following word problem:
Mr. Delaney broke his piggy bank with a sledge hammer and found that it only contained quarters and pennies. If he had a total of 120 coins for a combined value of $16.32, how many pennies did he have in his piggy bank?
x+y=120
0.25x+0.01y=16.32