Solving Linear Equations with Many Solutions

Select all the methods you can use to solve a system of equations

• Graphing

• Elimination

• Substitution

• Using a Table

• Desmos

Lines who's graphs intersect infinitely many times

• System of equations

• Coincident Lines

• Parallel Lines

• Perpendicular Lines

How many solutions does the following graph have?

• One solution

• Two solutions

• No solutions

• Infinitely many solutions

Two or more linear equations with the same variables

• Set of Linear Equations

• System of Linear Equations

• Process of Linear Equations

• Multiple Linear Equations

If a system of linear equations has infinitely many solutions, what does this mean about the two lines? 

• Intersecting lines

• Same line

• Parallel lines

The equation y = 3x + 5 has _____

• unique solution 

• Only two solutions

• Three solutions 

• Infinitely many solutions 

Determine the value of k if the equation has infinitely many solutions.

k(7x + 4) = 10 + 28x + 6

Mathematical Equivalence

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If a system of equations has infinitely many solutions, what do you know about the slopes and y-intercepts of the two equations?

• They have different slopes and different y-intercepts.

• They have the same slopes and different y-intercepts.

• They have the same slopes and the same y-intercepts.

• They have different slopes and the same y-intercepts.

3) Solve the system of linear equations.

• (3, 1, -5)

• (-3, 1, -1)

• no solution

• infinitely many solutions

4) Solve the system of linear equations.

• (1, -3, -4)

• (-1, 3, -4)

• no solution

• infinitely many solutions