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Solve by Graphing
Solve by Subsitution
Solve by Elimination
Things to Remember
Short Answer
100
In the form y=mx+b, what do the m and b represent?
m is the slope and b is the y-intercept
100
Solve the following system of equations by substitution: y=1 y=x
x=1, y=1
100
Solve the following system of equations by elimination x+y=10 x-y=2
x=6, y=4
100
What is the equation for finding the slope if you have two points on a line?
rise over run; y2 - y1 _____ x2 - x1
100
If both equations in a system have the same slope and y intercept, how many solution exist to the equations?
infinitely many or no unique solution
200
Put the equation 5x = -y +3 into the form y=mx+b
y=-5x+3
200
The price of admission to FunPark is $10. Each ride costs $5 dollars. Write an equation to model the amount of money you would spend at FunPark.
c=5r+10
200
You went to a carnival and spent a total of $16. It cost $4 to enter, $2 for each candy bar, and $3 for each game you played. Create an equation to model the cost of going to the carnival.
16=4 + 2c + 3g
200
Do parallel lines ever touch? And how does that effect the number of solutions they have in a system?
no - they have no solutions in a system
200
If a system of equations intersect at one point, how many solutions does it have?
one
300
Solve the system of equations by graphing: y=5 and y=x. You must show a graph to receive points
x = 5 y = 5
300
Solve the following system of equations by substitution: y=x+1 2x+y=7
x=2, y=3
300
Solve the system of equations by elimination: 4x-3y=-2 4x+5y=14
x=1, y=2
300
What are the equations for slope intercept form and standard form?
y= mx + b and Ax + By = C
300
If the equations in a system are equivalent (for example y = 2x + 3 and 2y = 4x + 6) then what do we know about their solutions?
there are an infinite amount of solutions because they are the same line
400
Solve the system of equations by graphing: y=2x and 2x=-y+12. You must show your graph to receive points.
x=3, y=6
400
Solve the system of equations by substitution: 4x=8y 2x+5y=27
Solve 4x=8y for x, and you get x = 2y. Substitute "2y" in for x in the 2nd equation 2(2y) + 5y = 27 and you get 9y=27 or y=3 x=6, y=3
400
Solve each system of linear equations by elimination: 3x-y=17 y+2x=8
x=5, y=-2
400
If we have two lines that are perpendicular, what do we know about their slopes?
They are opposite reciprocals of each other
400
If the equations in a system have the same slope, but different y-intercepts, how many solutions does it have?
none, because they are parallel.
500
Solve the system of equations by graphing: -x-2=-2y and 2x-4y-4=0
no unique solution because the lines will be parallel
500
Suppose you bought eight oranges and one grapefruit for a total of $4.60. Later that day, you bought six oranges and three grapefruits for a total of $4.80. Now you want to find the price of each orange and of each grapefruit. Write an equation for each purchase. Solve the system of equations.
8x+1g=4.60 6x+3g=4.80 x=.50, y= .60 each orange 50 cents, each grapefruit is 60 cents
500
A student can make a weekly salary of $200 plus 15% commission on sales at the Radio Barn or a weekly salary of $300 plus 10% on sales at Woofer, Etc. For what amount of sales do these two jobs pay the same? Write two equations and solve using elimination
i=.15s+200 i=.10s+300 0=.05s-100 100=0.05s $2000 in sales per week
500
Write two equations, one that has no solution in common with the line y = 5 and one that has exactly one solution with the line y = 5.
y = any number (will be parallel - no intersection and no solution) and x = any number. It will have an intersection point at (that number, 5)
500
Solve the following system of linear equations by substitution or elimination: y=4x+4 and -2x=(-1/2)y+4
The equations are equivalent, so there are an infinite number of solutions. When graphed, the equations are the same line.