Key Concepts
What is a system of equations?
Two or more equations with the same variables.
What is the mathematical meaning of the word "substitute?"
To replace a variable with an equivalent value or expression.
What should you do with the equations in a system if you are trying to use the Elimination Method to solve?
Add or subtract them
What is the first step when using a system of equations to answer a word problem?
Define variables
How do you find the solution to a system by graphing?
Graph the lines and locate their point of intersection.
What should you do first when solving this system using the Substitution Method?
x +2y=10
5x +10y=20
Solve the top equation for x by subtracting 2y from each side.
Which variable will be eliminated if these equations are subtracted?
3x+y=7
3x+2y=2
x
The measure of the larger of two complementary angles is 5 more than twice the smaller. Write a system of equations that could be used to find each angle measure. (x=measure of smaller angle, y= measure of larger angle)
x+y=90
y=2x+5
How many solutions does this system have?
y=3x-2
y = 3x+1
None!
What should you do to solve this system using the Substitution Method?
x = 3y-6
8x -2y=24
Replace x in the bottom equation with 3y-6.
What should you do to solve this system using Elimination?
x+y=8
x-y=10
Add the equations to eliminate y.
Adult tickets to a school play were $11 and student tickets were $6. If the total number of tickets sold was 235 and the total revenue was $2010, what system of equations could be used to find how many of each type of ticket was sold? (x = number of adult tickets, y = number of student tickets)
x+y=235
11x+6y=2010
When solving this system using Substitution, you found that x=2. What is the value of y?
y=3x-1
2x+y=9
What number should the bottom equation be multiplied by to solve this system using Elimination?
2x+3y=11
4x-y=1
Mr. Anderson is three times older than his son. His son is 34 years younger than he is. Write a system of equations that could be used to find each of their ages. (x = Mr. Anderson's age, y = son's age)
x=3y
y=x-34
What is the first thing you should do when solving the system below using the Elimination Method?
4x+6y=12
-4x=8y+16
Subtract 8y from each side to get the y's on the same side of the equation.
Solve this equation for y:
-6x+3y=18
y=2x+6
What number should each equation be multiplied by if you want to eliminate y?
3x-5y=-21
-6x-6y=-6
Kayak rentals cost $20 plus $15 per hour at Bob’s Kayak Shack, and cost $35 plus $10 per hour at Layla’s Water World. Write a system of equations to find the number of hours for which the cost of renting a kayak at both places is the same. (h = hours rented, c = total cost)
c=15h+20
c=10h+35