Exploring Systems of Equations with Substitution

What is the first step in solving a system of equations using substitution?

• Graph both equations.

• Multiply both equations by a common factor.

• Add the two equations together.

• Solve one of the equations for x or y.

In the first example, why was the second equation chosen to be rearranged?

• It had a larger constant term.

• It had a smaller coefficient for x.

• It did not have a variable multiplied by y.

• It was already in the correct form.

After substituting y = 2x - 9 into the first equation in the first example, what is the resulting equation?

• 3x + 2y = 10

• 3x + 2x - 9 = 10

• 3x + 2(2x - 9) = 10

• 2x - y = 9

What is the value of x in the first example after solving the substituted equation?

• 5

• 3

• 2

• 4

In the second example, what does the equation 24 = 24 indicate?

• Incorrect substitution

• Infinite solutions

• One solution

• No solution

What is the rearranged form of the first equation in the second example?

• y = 3x + 8

• y = -3x + 8

• y = 3x - 8

• y = -3x - 8

In the third example, what is the rearranged form of the second equation?

• x = -4y + 6

• x = 4y + 6

• x = 4y - 6

• x = -4y - 6

What does the false statement -6 = 4 indicate in the third example?

• One solution

• No solution

• Incorrect substitution

• Infinite solutions

If two lines are parallel, what does it mean for their system of equations?

• They intersect at one point.

• They have one solution.

• They have no solution.

• They have infinite solutions.

What topic will be discussed in the next lesson?

• Graphing systems of equations

• Substitution method

• Elimination method

• Matrix method