SOLVING LINEAR EQUATION BY SUBSTITUTION AND ELIMINATION

How to Solve Equations by Substitution Method

How to Solve Equations by Elimination Method

Problem 1 :

x = - 2y

x - y = 9

Solution :

x = - 2y ---> (1)

x - y = 9 ---> (2)

Substitute x = -2y in equation (2)

-2y - y = 9

-3y = 9

y = 9/-3

y = -3

By applying y = -3 in equation (1), we get

x = -2(-3)

x = 6

Therefore, the solution is x = 6 and y = -3.

Problem 2 :

3x + y = 7

-2x - y = 9

Solution :

3x + y = 7 ---> (1)

-2x - y = 9 ---> (2)

Add (1) + (2), we get

3x + y - 2x - y = 7 + 9

x = 16

By applying x = 16 in (1) equation, we get

3(16) + y = 7

48 + y = 7

y = 7 - 48

y = -41

Therefore, the solution is x = 16 and y = -41.

Solving System of Equations by Substitution Method

Solve each system by substitution.

Problem 1 :

 y = -3x + 4 and y = 4x - 10              Solution

Problem 2 :

y = -4x + 2 and y = 6x - 8       Solution

Problem 3 :

y = 2x and -6x + 3y = 16              Solution

Problem 4 :

y = -3x and 4x - 2y = -20              Solution

Problem 5 :

y = 3x - 4 and 4x + 3y = 1             Solution

Problem 6 :

y = x - 4 and -4x - 6y = -16            Solution

Problem 7 :

x = 3y + 1 and 2x + 4y = 12           Solution

Problem 8 :

 x = y - 4 and -2x + 3y = 6            Solution

Problem 9 :

Next week your math teacher is giving a chapter test. The test will consist of 35 questions. Some problems are worth 2 points and some problems are worth 4 points. There are 20 questions worth 2 points. How many problems of 4 points are on the test?

Solution

Problem 10 :

Next week your math teacher is giving a chapter test. The test will consist of 35 questions. Some problems are worth 2 points and some problems are worth 4 points. There are 20 questions worth 2 points. How many problems of 4 points are on the test?

Solution

Solving System of Equations by Elimination Method

Problem 1 :

3x + y = 7

-2x - y = 9

Solution

Problem 2 :

4x + 3y = 2

2x - 3y = 1

Solution

Problem 3 :

2x + 2y = 3

x = 4y - 1

Solution

Problem 4 :

y = 1 + x

2x + y = -2

Solution

Problem 5 :

1/2x + 4y = 4

2x - y = 1

Solution

Problem 6 :

y = x - 4

4x + y = 26

Solution

Problem 7 :

3x + 4y = -23

2y - x = -19

Waht is the solution (x, y) to the system of eqautions above ?

a)  (-5, -2)   b)  (3, -8)     c)  (4, -6)    d) (9, -6)

Solution

Problem 8 :

b = 2.35 + 0.25x

c = 1.75 + 0.40x

In the equation above b and c represent the price per pound in dollars, of beef and chicken respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken ?

Solution