# GMAT Quant: Algebra – Linear Equations

Linear equations are the type of equations whose all variables are of degree one. Linear equations that are collections of two or more linear equations are known as system of linear equation.

## Types of Linear Equation

• Independent: A linear system is said to contain independent linear equations if none of the equations can be derived from the other equation algebraically
• Consistent: If a system of linear equations has a solution, it is said to be consistent.
• Inconsistent: If it has no solution then the system of linear equations are inconsistent.

GMAT is never going to ask you simple questions of just two variables; rather they will be asking you questions that have more complex concept yet, the type of concept that uses some trick.

Let’s solve some questions and check the complexity level of aspirants facing in GMAT.

Question: The cost of 7 pears, 8 pineapples and 3 oranges is $20. The cost of 3 pineapples and 4 oranges and 5 mangoes is$21. The cost of 4 pears, 4 oranges and 6 mangoes is \$25. What is the cost of 1 pear, 1 pineapple and 1 orange and 1 mango?

Solution: According to question;

7P + 8PA +3 O = 20

3PA + 4 O + 5 M = 21

4P + 4 O + 6 M = 25

11P + 11 PA + 11 O + 11 M = 66

So, P + PA + O + M = 66/11 = 6

Question: If x+9 = 14, what is the value of (x-3)2?

1. 2
2. 4
3. 25
4. 49
5. 196

Solution: To get x-3, subtract 12 on both sides

So, x-3 = 2

Hence, (x-3)2 = 4

Question: If 3p+5q = 27, and p + 2q = 15, then q equals?

1. -21
2. -3
3. 9
4. 12
5. 18

Solution: 3p + 5q = 27

Substitute, 15-2q in place of p in first equation:

3(15-2q) + 5q = 27

45 – 6q +5q = 27

45 – q = 27

So, q = 18

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