Solving Equations Graphs

Solve the equation by graphing

5n + 34 = -2(1 - 7n)

• 0

• 3

• 4

• -6

How many solutions does the graph have?

• One solution

• No solution

• Infinite solutions

Answer explanation

These lines intersect at ONE point. This means that only one point will be true for the equations of both lines.

What does a "solution to a system of equations" mean?

• It's the point where both equations equal zero

• It's the point where graphs of both equations cross the y-axis

• It's the point that is true for both equations at the same time

• It's the point where graphs of both equations cross the x-axis

Answer explanation

A solution to a system of equations is a point that will work in all equations within the system.

Which answer has a correct first step for solving this system without graphing:

• The variable is already isolated, so we've already solved the system.

• The variable is already isolated for y, so we substitute it in the first equation and solve for x

  3x + 3(3x + 5) = 3

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• The variable is already isolated for y, so we substitute it in the second equation and solve for x

  y = 3(3x + 3y) = 3

Answer explanation

$3x+3y=3$

$y=3x+5$
A variable is already isolated here, so we already have an equivalent expression from the second equation that can be substituted in place of y in the first equation.

How many solutions does the following graph have?

• One solution

• Two solutions

• No solutions

• Infinitely many solutions

The solution to the system of linear equations is...

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

How many solutions does the following graph have?

• One solution

• Two solutions

• No solutions

• Infinitely many solutions