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.

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

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

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

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

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

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

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

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

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

Solving System of Equations by Elimination Method

1)  4x + 3y = 2 and 2x - 3y = 1        Solution

2)  2x + 2y = 3 and x = 4y - 1        Solution

3)  y = 1 + x and 2x + y = -2        Solution

4)  1/2x + 4y = 4 and 2x - y = 1        Solution

5)  y = x - 4 and 4x + y = 26            Solution