Types of Solutions
The three possible types of solutions for a system of two linear equations.
What is no solution, one solution and infinitely many solutions?
Set up the following system of equations using substitution:
y= 2x – 2
2x+3y=18
What is 2x+3(2x-2)=18?
Two common methods for solving systems of two linear equations algebraically.
What is Substitution and Elimination?
What is Natural, Whole, Integer, Rational, Irrational, Real?
True or False: If two lines have the same slope but different y-intercepts, the system has no solution. Explain.
What is True? Same slopes = parallel lines; different intercepts → never intersect → no solution.
The Type of Solution that has parallel lines.
What is no solution?
This is what you may need to do when you do not see a variable that eliminates at first.
What is multiply one or both equations to create opposite coefficients?
The first algebraic step you do after solving one equation for a variable
What is substitute that expression into the other equation to solve for a variable?
152
What is 225?
A system has infinitely many solutions. What does this tell you about the equations? Give an example.
What is the equations represent the same line?
You graphed two equations but they appear to have the same line.
What is Infinitely Many Solutions?
Use substitution to solve: x=3y−1 and 2x+y=7
What is (4,3)?
Explain the reason you might choose elimination over substitution for the system 3x+7y=11 and 6x−7y=4
What is the coefficients of y are opposites?
The y-intercept in the equation: y=4x-6
What is -6?
x+y=7
x+y=-7
What is No Solution?
Two lines intersect at a point.
What is one solution?
Describe both ways that you could multiply the first equation by a number to eliminate x and/or y. 3x−2y=7
6x+4y=10
Multiply the first equation by 2 or by -2.
Which variable eliminates in this system of equations x+y=6 and x−y=2
What is y?
The cost to rent a bike is a $5 flat fee plus $2 per hour. Write an equation for total cost C in terms of hours h
What is C=2h+5?
Two friends share the cost of a pizza. One friend pays $3 more than the other. Together they paid $15. How much did each friend pay?
The solution to y=2x+1 and y=2x−3.
What is No Solution?
Same Slope; Different Y-Intercept
After solving a system of equations using substitution or elimination the result is 0=0. Name the solution type and explain your reasoning.
What is Infinitely Many Solutions? Reason: It makes a true statement.
For the system 2x+3y=8 and 4x+6y=16 explain what the result tells you about the number of solutions and why.
What is Infinitely Many Solutions?
Create a word problem that requires setting up a system of equations.
Answers may vary
Two friends are selling lemonade. Friend A charges a $1.50 flat fee plus $0.75 per cup. Friend B charges no flat fee but $1.25 per cup. After how many cups are the total costs equal? Set up and solve a system to justify your answer.
What is 3 cups?