# SUBSTITUTION METHOD SOLVING SYSTEMS OF EQUATIONS

Substitution Method Solving Systems of Equations

In this section, you will learn how to solve system of linear equations with two unknowns using substitution.

## Substitution Method Solving Systems of Equations - Problems

Problem 1 :

Solve the following system of equations by substitution method.

2x - 3y = -1  and  y = x - 1

Solution :

2x - 3y  =  -1 -----(1)

y  =  x - 1 -----(2)

Step 1 :

From (2), substitute (x - 1) for y into (1).

(1)-----> 2x - 3(x - 1)  =  -1

Simplify.

2x - 3x + 3  =  -1

-x - 3  =  -1

-x  =  2

Multiply each side (-1).

x  =  -2

Step 2 :

Substitute -2 for x into (2).

(2)-----> y  =  2 - 1

y  =  1

Therefore, the solution is

(x, y)  =  (-2, 1)

Problem 2 :

Solve the following system of equations by substitution method.

y = -3x + 5  and  5x - 4y = -3

Solution :

y  =  -3x + 5 -----(1)

5x - 4y  =  -3 -----(2)

Step 1 :

From (1), substitute (-3x + 5) for y into (2).

(2)-----> 5x - 4(-3x + 5)  =  -3

Simplify.

5x + 12x - 20  =  -3

17x - 20  =  -3

17x  =  17

Divide each side by 17.

x  =  1

Step 2 :

Substitute 1 for x into (1).

(1)-----> y  =  -3(1) + 5

y  =  -3 + 5

y  =  2

Therefore, the solution is

(x, y)  =  (1, 2)

Problem 3 :

Solve the following system of equations by substitution method.

y = 5x - 7  and  -3x - 2y = -12

Solution :

y  =  5x - 7 -----(1)

-3x - 2y  =  -12 -----(2)

Step 1 :

From (1), substitute (5x - 7) for y into (2).

(2)-----> -3x - 2(5x - 7)  =  -12

Simplify.

-3x - 10x + 14  =  -12

-13x + 14  =  -12

Subtract 14 from each side.

-13x  =  -26

Divide each side by -13.

x  =  2

Step 2 :

Substitute 2 for x into (1).

(1)-----> y  =  5(2) - 7

y  =  10 - 7

y  =  3

Therefore, the solution is

(x, y)  =  (2, 3)

After having gone through the stuff given above, we hope that the students would have understood, how to solve system of linear equations by substitution method.

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