Solving Linear-Quadratic Systems

Solving Linear-Quadratic Systems

Linear Systems can have the following types of solutions

Infinite Solutions

• Means that both equations are the same.
• Any point you pick on the line will both be a solution to the linear equations

One Solution: (-2,1)

• Both linear equations cross at one point on the graph.

No Solutions

• Means that lines do not cross. EVER

Multiple Choice

Click on the graph and determine the solutions of the system of equations.

• Infinite Solutions

• One Solutions: (3,1)

• No Solutions

• Two Solutions: 3 & 1

Multiple Choice

A system of equations when graphed are parallel to each other, determine what type of soultions they have.

• No Solution

• Infinite Solution

• One Solution

• Multiple Solutions

Fill in the Blanks

An

solution means that the system of equations has the same equation.

Linear-Quadratic Systems can have the following types of solutions.

Two Solutions: (0,-2) and (3,1)

• System of equations cross at two points on the graph

One Solution: (1,-3)

• System of equations meet at one point on the graph

No Solution

This means that both equations NEVER intersect

Fill in the Blanks

If a linear equation and a quadratic equation never intersect then the system of equation have

.

Multiple Choice

If the a quadratic equation crosses the linear equation at two points on a graph, then the system of equations has?

• No solution

• One solution

• Two solution

• All real numbers

Multiple Choice

A linear-quadratic system touch at the point (1,-3) is said to have how many solutions?

• Two solutions

• One solution

• No solution

• Many solutions

​Find the number of solutions algebraically. ( substitution)

Multiple Choice

Determine the number of solutions to the given linear-quadratic system.

• 0 solutions

• 1 solution

• 2 solutions

• 3 solutions

Multiple Choice

What are the solutions to the graphed system?

• (0,-2) and (-3,1)

• (-2,0) and (2,0)

• (0,-2) and (3,1)

• (2,2) and (1,0)

Multiple Choice

Solve the system of linear and quadratic equations:

y = 5

y = 2x² - 16x + 29

• (6, 5) and (2, 5)

• (2, 6)

• (6, 2)

• (5, 6) and (5, 2)

Multiple Choice

Find the solution.

• (2,3) and (3,4)

• (-3,-15) and (4,-8)

• (-3,10) and (8,4)

• (-8,3) and (-4,10)

Multiple Choice

Find the solution:
y = x² - 4x + 6
y = x + 2

• (3, 1) and (6, 4)

• (-1, 1) and (4, 2)

• (1, 3) and (4, 6)

• (1, 4) and (3, 6)