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

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.

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.

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.

• Add 5 to both sides.

• Divide both sides by 2

• 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.

• Add 8 to both sides.

• Divide both sides by 4.

• Break it into two cases.

• Add 7 to both sides.

• Subtract 1 from both sides.

• Divide both sides by 3.

Answer explanation

This is the "Less ThAND" case.

• Subtract 2 from both sides

• Divide both sides by 5

Answer explanation

This is the "GreatOR" case.

• Divide both sides by 5.

• Distribute 5 through.

• Set up two cases.

• Add 5 to both sides.

• Divide both sides by -4 and change the inequality sign to face the other direction.

• Add 4 to both sides.

• Add 9 to both sides.

• Distribute -4 through the absolute value.