Systems of Equations

What is the solution to the systems of equations shown in the graph?

• 1 Solution x=-1/2

• 1 Solution y=-1/2

• Many Solutions

• No Solution

What is the solution?

• (1, -1)
• (-1, 1)
• (0, -2)
• (2, 0)

What is the solution?

• One Solution
• No solution
• Infinitely Many Solutions
• (0, -1.5)

To solve the system by elimination, you should
x-2y=1
x+4y=7 

• add the 2 equations together

• subtract the second equations

• substitute the 2nd equation into the first

Answer explanation

Remember if the coefficient on the liker terms is exactly the same, we subtract the entire second equation

When you solve the system by elimination, you should subtract the second equation
x-2y=1
x+4y=7 

Which is correct?

• x-2y=1
  -x+4y=7 

• x-2y=1
  - x+ - 4y= - 7 

• x-2y=1
  - x+ - 4y=7 

Answer explanation

Remember if the coefficient on the liker terms is exactly the same, we subtract the entire second equation. You need to change the entire second equation into its opposite

When Sarah solved a system using substitution, she got 4 = 5. What can Sarah conclude?

• The solution is (4,5)

• There are infinitely many solutions

• Sarah made a mistake

• There is no solution

Answer explanation

4 can never equal 5, so there is NO possible solution. The equations will never overlap

The ordered pair that satisfies BOTH equations in the system is called the _____________________

• system of equations
• function
• graph
• solution 

When Sam solved a system using substitution, he got 0 = 0. What can Sam conclude?

• The system of equations does not have a solution.

• The work must be incorrect because it is not possible to get this equation.

• The solution is (0,0)

• The system of equations has infinitely many solutions.

Answer explanation

0 ALWAYS equals 0, so every possible solution is a solution, therefore there are INFINITE solutions

Answer explanation

Need help? check out this video

https://youtu.be/uzyd_mIJaoc?si=5-94ryL2Y8HWLIcF