Aim How do we solve systems of equations that represent real world problems?
Warm Up
1.Which is the bestway to solve following system of equations?
2x – 2y = 16
y = 3x + 12
A)Substitution, because you can easily substitute an expression for x.
B)Substitution, because you can easily substitute an expression for y.
C)Elimination, because there are coefficients that are opposites.
D)Elimination, because there are coefficients that are the same.
2.Which is the bestway to solve following system of equations?
-2x = -20
2x + y = 25
A)Substitution, because you can easily substitute an expression for x.
B)Substitution, because you can easily substitute an expression for y.
C)Elimination, because there are coefficients that are opposites.
D)Elimination, because there are coefficients that are the same.
3.Which is the bestway to solve following system of equations?
3x + y = -9
5x + y = -15
A)Substitution, because you can easily substitute an expression for x.
B)Substitution, because you can easily substitute an expression for y.
C)Elimination, because there are coefficients that are opposites.
D)Elimination, because there are coefficients that are the same.
Group Work
Write and solve a system of linear equations to solve each problem below.
1.April and Andy went to a bagel shop. April bought 2 bagels and one cup of coffee for $5. Andy bought 5 bagels and 3 cups of coffee for $14. What is the cost of a bagel and the cost of a cup of coffee?
2.Buster and Tobias work at a frozen banana stand. They each get paid the same hourly wage and the same extra amount for every frozen banana that they sell. Buster worked 10 hours, sold 100frozen bananas and earned $140. Tobias worked 10 hours, sold 70frozen bananas and earned $125. How much do they earn per hour and how much do they get for every frozen banana that they sell?
3.At a bakery 2 brownies and 4 cookies cost $2. 1 brownie and 6cookies cost $2. What is the cost of a brownie and the cost of a cookie?
.
4.Which is not trueabout the following system of equations?
y = 2x + 3
y = 2x –5
A)They have the same slope.B)They are parallel.
C)They have infinite solutions.D)They have no solution.
5.Which is not trueabout the following system of equations?
y = 3x + 1
y – 3x = 1
A)They have the same slope.B)They are the same line.
C)They have infinite solutions.D)They have no solution.
6.Which is the bestway to solve following system of equations?
3x –y = -12
2x + y = 17
A)Substitution, because you can easily substitute an expression for x.
B)Substitution, because you can easily substitute an expression for y.
C)Elimination, because there are coefficients that are opposites.
D)Elimination, because there are coefficients that are the same.
7.Which is the bestway to solve following system of equations?
2y + 2x = 40
x = 5y
A)Substitution, because you can easily substitute an expression for x.
B)Substitution, because you can easily substitute an expression for y.
C)Elimination, because there are coefficients that are opposites.
D)Elimination, because there are coefficients that are the same.
8.Which is the bestway to solve following system of equations?
y = 4x – 4
2x + 2y = 24
A)Substitution, because you can easily substitute an expression for x.
B)Substitution, because you can easily substitute an expression for y.
C)Elimination, because there are coefficients that are opposites.
D)Elimination, because there are coefficients that are the same.