Solving Non-Linear Systems with the Substitution Method

The video tutorial explains how to solve non-linear systems of equations using the substitution method. It covers three cases: two solutions, one solution, and no solution. Each case is demonstrated with an example, showing how to set equations equal, manipulate terms, and solve for variables. The video concludes with a summary of the solutions found for each example.

What method is being used to solve the non-linear system of equations in this video?

• Elimination method

• Substitution method

• Graphical method

• Matrix method

In the first example, what is the first step after setting the equations equal to each other?

• Divide both sides by a constant

• Add or subtract terms to get all terms on one side

• Multiply both sides by a constant

• Take the square root of both sides

What are the two solutions for x in the first example?

• x = 3 and x = -2

• x = -3 and x = 2

• x = 4 and x = -1

• x = -4 and x = 1

What is the corresponding y-value when x = -4 in the first example?

• y = -11

• y = 11

• y = 1

• y = 3

In the second example, what is the value of y given by the second equation?

• y = -5

• y = 0

• y = 5

• y = 10

What is the solution for x in the second example?

• x = 0

• x = -1

• x = 1

• x = 5

What is the ordered pair solution for the second example?

• (0, 5)

• (0, 0)

• (5, 0)

• (5, 5)

In the third example, what is the first step after setting the equations equal to each other?

• Take the square root of both sides

• Add or subtract terms to get all terms on one side

• Divide both sides by a constant

• Multiply both sides by a constant

Why is there no solution in the third example?

• The equations are identical

• The equations are parallel

• The quadratic equation cannot be factored

• The equations have the same y-intercept

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