1. Write the system so the like terms are aligned.
2. Add or subtract the equations to eliminate a variable. Then solve.
3. Substitute the value from Step 2 into one of the equations to solve for the other variable.
4. Write your answer as ordered pair.
100
Steps of elimination when the variables will not cancel right away.
1) Multiply at least one equation by a constant
2) Add or subtract the equations to eliminate a variable. Then solve.
3) Substitute the value from Step 2 into one of the original equations to solve for the other variable.
4)Write your answer as an order pair.
100
Where is the solution to a system of inequalities?
The section of the graph that overlaps.
200
Answer to the system if the two lines do not intersect.
What is no solution?
200
Steps of substitution
1. Solve one equation for a variable.
2. Substitute the expression from Step 1 into the other equation in place of the variable. Solve the equation.
3. Substitute the value from Step 2 into either equation to solve for the other variable.
200
Operation to use when the coefficients have opposite signs (one is positive, one is negative)
What is addition?
200
What do you need to multiply by to get a variable to cancel?
5x + 6y = -8
2x + 3y = -5
Multiple the second equation by 2 to cancel the y's.
200
Steps for graphing a system of inequalities.
1) Graph the first inequality just as you would graph an equation. Remember to use a solid or dashed line.
2) Use a point test to determine what side of the line you should shade.
3) Repeat steps 1 and 2 for the second inequality.
4)The overlapped section will be the solution.
300
Answer to the system if there are two different forms of the same equation (always overlapping)
What is infinite solutions?
300
When your variables disappear and you are left with a true statement.
What is infinite solutions?
300
Operation to use when the coefficients have the same sign (both positive or both negative)
What is subtraction?
300
What do you need to multiply by to get a variable to cancel?
4x + 2y = 8
3x + 3y = 9
To cancel the x's, multiply the top equation by 3 and the bottom equation by 4.
To cancel the y's, multiply the top equation by 3 and the bottom equation by 2.
400
Graph the system of equations and determine the number of solutions. If there is one solution, name it.
y = -3x + 10
y = x - 2
One solution; (3,1)
400
Solve the system of equations using substitution.
y = 2x + 1
3x + y = -9
(-2, -3)
400
Solve the system of equations using elimination.
-4x + 3y = -3
4x - 5y = 5
(0, -1)
400
Solve the system of equation using elimination.
9x + y = 13
3x + 2y = -4
(2, -5)
400
Name one ordered pair that is a solution to the system of inequalities that is shown and name one ordered pair that is not a solution.
Multiple answers.
500
Graph the system of equations and determine the number of solutions. If there is one solution, name it.
y = -2x - 5
y = -2x + 3
No solution
500
Use substitution to solve the system of equations.
x + 2y = 6
3x - 4y = 28
Solve the system of equations using elimination.
5x - 3y = 6
2x + 5y = -10
(0, -2)
500
Write the two inequalities for the given situation.
An economics class formed a company to sell notebooks and pens. Each notebook cost $2.50 and each pen cost $1.25. They would like to sell more than 50 items per week, with a goal of earning more than $60 per week.
n = # of notebooks
p = # of pens
n + p > 50
2.5n + 1.25p > 60