Systems of Equations Test Review

Systems of Equations Test Review

Systems of Equations

• 2 or more equations with the SAME variables

• The solution to a system will make ALL of the equations TRUE

• There are 3 ways to find the solution: Graphing, Substitution or Elimination

Graphing

Where do your equations (lines) intersect?

Multiple Choice

What is the solution?

• (3, -2)

• (-2, 3)

• no solution

• infinitely many

Don't forget.... we still need the other variable!

once you find the first variable, take that value and substitute it into either equation and solve for the other variable

Write your answer as an ordered pair!

Multiple Choice

Which of the following correctly shows substitution being set up?

y=3x

x + y = -32

• x + 3x = -32

• y + y = -32

• y= 3(x + y = -32)

Multiple Choice

Use substitution to solve:

y= 3x

x + y = -32

• ( -8, -24)

• (24, 6)

• (8, 24)

• ( -8/3, -8)

Multiple Choice

Use elimination to solve:

 $\ \ 7x+y=-9$  

 $-3x-y\ =5$  

• no solution

•  $\left(-2,-3\right)$  

•  $\left(1,8\right)$  

•  $\left(-1,-2\right)$  

Multiple Choice

Are we ready to eliminate?

 $x\ +\ y\ =\ 6$  

 $x+y\ =5$  

• yes

• no

To eliminate we need one variable to become zero

• we might need to multiple by -1

• we might need to multiply one equation by a factor of the second equation

• we might need to multiply both equations (if this is the case, make it easy on yourself and flip flop your numbers)

• DON'T EVER FORGET THAT OUR GOAL IS TO MAKE ONE VARIABLE TO GO AWAY

Multiple Choice

Use elimination to solve:
 $4x-2y=4$  

 $2x+y=6$  

•  $\left(2,\ 2\right)$  

•  $\left(\frac{6}{10},\ \frac{3}{10}\right)$  

•  $\left(5,\ 4\right)$  

• infinitely many solutions

Systems of Inequalities

• your solutions are where your shading overlaps

Multiple Choice

What is a possible solution of this system of inequalities?

• $\left(-9,\ 3\right)$

• $\left(5,\ 0\right)$

• $\left(0,\ 10\right)$

• $\left(-2,\ -10\right)$

Poll

How ready are you for this test?

• Bring it on!

• After my deltamath practice I will be golden

• I will be coming to academic support before the test