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The First Step: Systems and Abs. Value Equations/Inequalities

Authored by Bo Gilbert

Mathematics

12th Grade

Used 2+ times

The First Step: Systems and Abs. Value Equations/Inequalities
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10 questions

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1.

MULTIPLE CHOICE QUESTION

2 mins • 10 pts

Consider the system below:

2x - y = 10

4x + y = 8

What is the first step in solving this system using elimination?

Add the systems together to cancel out the y-variable.

Subtract 4x from both sides of the second equation.

Subtract the bottom system from the top.

Multiply the top system by 2 to have the x-variables cancel out.

Answer explanation

This is the best answer, since adding the systems together will immediately cancel out the y-variables.

2.

MULTIPLE CHOICE QUESTION

2 mins • 10 pts

Consider the following system:

2x + y = 12

3x + 3y = 9

What would be your first step if trying to solve the system by substitution?

Subtract 2x from both sides of the top equation to isolate the y-variable.

Multiply the top system by -3.

Add the systems together.

Subtract 3x from both sides of the bottom equation to isolate 3y.

Answer explanation

This is the best answer because you are able to immediately isolate the y-variable.

3.

MULTIPLE CHOICE QUESTION

2 mins • 10 pts

Consider the following system:

2x - 3y = 9

4x - 5y = 12

What is the first step in solving this system by elimination?

Multiply the top equation by 2 (or -2) to have the x-variables match.

Add 3y to both sides of the first equation.

Find the least common multiple of 3 and 5.

Add 5y to both sides of the second equation.

Answer explanation

This is the best answer, because you only need to multiply one of the equations by a value to get the x-variables to match.

4.

MULTIPLE CHOICE QUESTION

2 mins • 10 pts

Add 5 to both sides.

Divide both sides by 2

5.

MULTIPLE CHOICE QUESTION

2 mins • 10 pts

Divide both sides of the equation by 3.

Distribute the 3 through the absolute value expression.

Break this into two cases.

Add 9 to both sides.

Answer explanation

You cannot distribute a number through an absolute value function.

6.

MULTIPLE CHOICE QUESTION

2 mins • 10 pts

Add 8 to both sides.

Divide both sides by 4.

Break it into two cases.

Add 7 to both sides.

7.

MULTIPLE CHOICE QUESTION

2 mins • 10 pts

Subtract 1 from both sides.

Divide both sides by 3.

Answer explanation

This is the "Less ThAND" case.

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