Linear Equations

Question 1

What is a linear equation?

Answer 1

Expression that has an equal sign to the power of 1.

Question 2

What 2 strategies are used to solve linear equations?

Answer 2

Substitution and Combination

Question 3

What is the key to solve | absolute value | equations?

Answer 3

Set the value inside the || to equal both the positive and negative. Solve for both.

Ex.
Solve 12 + | 4-w | = 18

1. 4-w = 6
2. 4-w = -6

Question 4

How do you use a combination to solve?

Answer 4

Multiply one equation by a number that (when added or subtracted) will eliminate one or more variables from the other equation.

EX.
Solve for X and Y
x + y = 9
2x = 5y + 4

1. Multiply the top equation by (-2) then add the two equations to eliminate the x variable.
2. Solve for y
3. Plug back y to solve for x

Question 5

GMAT Trick for system of equations: When given two equations and the thought is to combine or substitute, what is the trick GMAT will make?

Answer 5

Both equations simplify to the same equation and therefore the variable cannot be solved.

EX.

What is the value of x?

(1) 2x – 5y + 6 = 12
(2) 8x – (4x + 10y) + 27 = 39