Non-Linear Systems Test Review

Which of the following statements are true about a non-linear system of equations in two variables?

• The system contains at least one non-linear equation.

• The system will have no solutions or one or more solutions.

• There are three methods to solve a system.

• All of these statements are true about a non-linear system of equations in two variables.

Which of the following are the steps to solve a non-linear system of equations in two variables by graphing?

• 1. Graph both of the equations on the same graph.

  2. Find the intersection points of the graphs.

  3. The intersection points are your solutions.

• 1. Subtract one equation from the other equation.

  2. Graph the resulting equation.

  3. The x-intercept of the graph is your solution.

• 1. Graph only one of the equations.

  2. Find your y-intercept of the graph.

  3. The y-intercept is your solution.

• 1. Graph both equations on the same graph.

  2. Find the points where the graphs cross the x-axis.

  3. These points are your solutions.

Which of the following are the steps we take to solve a non-linear system of equations in two variables x and y using substitution?

• 1. Substitute one equation for the other.

  2. Solve the resulting equation for x.

  3. This is your solution.

• 1. Solve for y in one of the equations.

  2. Plug the expression you found for y into the other equation, and solve for x.

  3. Plug the values you found for x into either of the original equations to find the corresponding value of y for each value of x.

  4. These are your solutions.

• 1. Subtract one equation from the other equation.

  2. Substitute the resulting equation in for one of the original equations.

  3. Solve one of the equations in the new system for x.

  4. The value of x is the solution to the system.

• It is impossible to solve a non-linear system of equations in two variables with substitution.

Which of the following are the steps we take to solve a non-linear system of equations in two variables using elimination?

• 1. Subtract one equation from the other equation.

  2. Substitute the resulting equation in for one of the original equations.

  3. Solve one of the equations in the new system for x.

  4. The value of x is the solution to the system.

• 1. Find opposite terms.

  2. Add the equations to each other.

  3. Solve the resulting equation for x or y (whichever is there).

  4. Plug the values for x or y you found into either of the original equations to find the corresponding x or y value.

• 1. Solve for y in terms of x in one of the equations.

  2. Plug the expression you found for y into the other equation and solve for x.

  3. Plug the values you found for x into either of the original equations to find the corresponding value of y for each value of x.

• It is impossible to solve a non-linear system of equations in two variables with elimination.

 $y=x^2-4$  

 $y=-x-2$  

Match the system of equations with its graph.

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 $y=x^2-2x+2$  

 $y=2x-2$  
Solve the system of non-linear equations by graphing. Use DESMOS!

• (2, 2)

• (-2, 0) and (1, -3)

• No Solutions

• (-1, -4) and (4, 6)

 $x^2+y^2=16$  
 $x+y=4$  
Solve by graphing. Use DESMOS!

• (-4, 0) and (4, 0)

• (0, 4) and (0, -4)
  

• No Solutions

• (0, 4) and (4, 0)

 $x^2+y^2=100$  

 $y-x=2$  
Solve using substitution.

 $y=x^2-7x+2$  
 $2x+y=2$  
Solve using substitution. 

 $x^2+y^2=34$  
 $x^2-2y^2=7$  

Solve using elimination