Graphs of Systems of Equations

Systems of Equations Recap

What is a system of equations?

Two or more equations simultaneously

Can be found from the intersection of the graphs!

In our case, the solution to the system is the point (1, 2)

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Solution(s) to Systems

Multiple Choice

What is the solution to the system?

$$2x+3y=6$$

$$2x-y=6$$

• (0, 2)

• (6, 6)

• (3, 0)

• (2, 3)

Multiple Choice

What is the solution to the system?

$$3y-x=-3$$

$$3y+2x=15$$

• (0, 5)

• (7.5, 0)

• (1, 6)

• (6, 1)

Multiple Choice

What is the solution to the system?

$$y=4x+5$$

$$y=-x-5$$

• (-3, -2)

• (-5, 0)

• (-2, -3)

• (0, 5)

Multiple Choice

What is the solution to the system?

$$3x-2y=6$$

$$x+y=-3$$

• (-3, 0)

• (0, -3)

• (2, 0)

• (0, 2)

Another example

Multiple Select

Select all solution(s) to the system

$$y\ =\ x^2-3x-4$$

$$y=-x-1$$

• (-1, 0)

• (4, 0)

• (3, -4)

• (0, -4)

Multiple Select

Select all solution(s) to the system

$$y\ =\ -x^2-4$$

$$y=2x-4$$

• (2, 0)

• (-2, -8)

• (-8, -2)

• (0, -4)

Multiple Select

Select all solution(s) to the system

$$y\ =\ -\left(x+1\right)\left(x-2\right)$$

$$y=2$$

• (2, 0)

• (-1, 0)

• (0, 2)

• (1, 2)

Multiple Select

Select all solution(s) to the system

$$y\ =\ -\left(x+1\right)\left(x-2\right)$$

$$y=2$$

• (-3, -2)

• (-1, 0)

• (-2, -3)

• (0, 1)