Non-linear equations (multi-variable)

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 equations could be used to solve:
y = x² + 3x - 5
y = x + 3

• x² - 3x + 5 = x - 3
• x² + 3x - 5 = x + 3
• x² + 3x - 5 + x + 3 = 0
• x² + 3x - 5 = 0

• one solution

• no solutions

• infinitely many solutions

• two solutions

Find the solution.

• x = 56, 29

• x = 35, -12

• x = 15, 2

• No Solution

Find the solution(s) to the system.

• (0,-3)(-1,-2)

• (0,-3)

• (-2,0)(2,0)

• No solution

What is/are the y-coordinates of the following system?:

 $2x^2-3x-y=-5$  
 $-x+y=5$  

•  $y=0,\ 2$  

•  $y=5,\ 7$  

• No Solutions

Which of the following are TRUE about systems of linear equations? Select all that apply.

• There must be at least 3 equations in a system.

• All equations must be linear (straight lines).

• All equations must have the same variables.

• All equations must have "x" and "y" specifically.

Find the exact real solutions to the system

• no real solutions

• (0, 5)

• (-10, 11)

• (5, 0)

Solve by substitution.  Check the solution(s).

 $x+y=1\ \ \ \ \ \$ 

 $y=x^2-5$   

• (-3, 4)

• (2, -1)

• (3, -2)

• (-2, 3)