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Methods
Vocabulary
Explaining in Math
Solving Equations
Real Life Problems
100
True or False? Each system of equations can be solved using only 1 method.
False
100
Two equations that are to be solved together
What is a system of equations
100
Describe the solution of a system of equations if the sum of the equations is 0 = 2.
The result of the statement is false, so there is no solution.
100
Solve this system: 2x + 3y = 12 2x - y = 4
(3,2)
100
Peter spent $16 for 12 pieces of candy. Each chocolate bar costs $2, and each lollipop costs $1. Determine how many of each he bought.
4 chocolate bars and 8 lollipops
200
This method is best if one of the variables has exactly the same coefficient in the two equations.
What is elimination using subtraction
200
A system that has at least one solution is said to be ______.
What is consistent
200
Explain how you could recognize a system of linear equations with infinitely many solutions without seeing its graph.
One of the equations will be a multiple of the other.
200
Solve this system: -1 = 2x - y 8x - 4y = -4
infinitely many solutions
200
The drama club is selling tickets to their spring musical. Adult tickets are $4 and student tickets are $1. A total of 285 tickets are sold for $765. How many of each type of ticket are sold?
160 adult tickets and 125 student tickets
300
This method is best if you don't necessarily need an exact solution.
What is graphing
300
What do we know about the two lines if they have no solution?
They are parallel.
300
Describe when it would be most beneficial to use elimination with addition or subtraction to solve a system of equations.
Use when one variable in both equations has either the same coefficient or opposite coefficient.
300
Solve this system: 3j + 4k = 23.5 8j - 4k = 4
(2.5, 4)
300
MRA put on a bake sale. They charged $10 per pie and $8 per cake. They sold 40 items and brought in $356. How many pies and how many cakes did the school sell?
18 pies and 22 cakes
400
This method is best if one of the variables in either equation has a "hidden" coefficient of 1.
What is substitution
400
If the two equations graph as the same line, what is the solution?
Infinite solutions
400
Explain how to determine what to substitute when using the substitution method of solving systems of equations.
When you have an equation that contains "x =" or "y =", simply substitute the expression on the other side of the equal sign into either one of the equations for either x or y.
400
Solve this system: 12x - 3y =-3 6x + y = 1
(0,1)
400
At the fair, the cost for 4 slices of pizza and 2 orders of French fries is $21. The cost of 2 slices of pizza and 3 orders of fries is $16.50. Find out the prices for a single slice of pizza and a single order of fries.
pizza: $3.75 fries: $3.00
500
This method is a last resort when nothing else will work.
What is elimination using multiplication, then addition or subtraction.
500
If a system has exactly one solution, it is said to be ___________ and _____________.
What is consistent and independent
500
Describe the advantages and disadvantages to solving systems of equations by graphing.
Graphing clearly shows whether a system has one solution, no solution, or infinitely many solutions. However, finding the exact values of x and y from a graph can be difficult.
500
y + 4x = 3 y = -4x - 1
no solution
500
Peyton saved dimes and quarters in his piggy bank. He had $4 and 25 coins. Determine how many quarters and how many dimes make up his savings.
15 dimes, 10 quarters