Solve for X Using Substitution

Introduction to solve for x using substitution:
Algebra is the one of the branch in mathematics. In which the numbers, variables are used to to form the equation. the variable are unknown. In algebra there are many way to find the unknown variable in the equation. in which the substitution is the one method, used to find the unknown variable.The substitution is a method, which is used solve the problem in algebra. In this method the variable obtained form on equation and substitute that value in another equation.

Solve for X Using Substitution-substitution Method:

Suppose we are given two linear equations in x and y

Step l: Express y in terms of x in one of the given equations.

Step 2: Substitute this value of y in the other equation.

Step 3: Solve the equation obtained in step 2 and find the value of x.

Solve for X Using Substitution-problems:

Problem 1:

Find the value of x from the given set equation:3x+y=3, 5x-2y=16

Solution:

The given equation are

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

5x-2y=16------------(2)

Step l: Express y in terms of x in one of the given equations.

From (1) we get, 3x+y=3

Y = 3-3x----(3)

Step 2: Substitute this value of y in the other equation.

Substituting y=3-3x in the equation (2), we get

5x-2(3-3x) =16

Step 3: Solve the equation obtained in step 2 and find the value of x.

5x-6+-6x=16

5x+6x=16+6

11x=22

X=`22/11`

X=2.

Problem 2.

Find the value of x from the given set equation: 3x+2y=17, 2x-3y=-6

Solution:

The given equations are

3x+2y=17-------------(1)

2x-3y=-6------------(2)

Step l: Express y in terms of x in one of the given equations.

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From (1) we get, 3x+2y=17

2y = 17-3x

y=`1/2` (17-3x)----(3)

Step 2: Substitute this value of y in the other equation.

Substituting y=`1/2` (17-3x) in the equation (2), we get

2x-3( `1/2` (17-3x))=-6

Step 3: Solve the equation obtained in step 2 and find the value of x.

2x-`3/2` (17-3x) =-6

Multiplying both sides by 2

2 * 2x-2 * `3/2` (17-3x) =2x (-6)

4x-3(17-3x) =-12

4x-51+9x=-12

4x+9x =-12 +51

13 x = 39

x=3

Problem 3:

Solve the following pair of equations by substitution method:

7x – 15y = 2 -------- (1)

x + 2y = 3------------ (2)

Solution:

Step 1 :  write one variable in terms of the other.

Let us consider the Equation (2) :

x + 2y = 3

And write it as x = 3 – 2y -------(3)

Step 2: Substitute the value of x in Equation (1). We get

7(3 – 2y) – 15y = 2

i.e., 21 – 14y – 15y = 2

i.e., – 29y = –19

Therefore, y =`19/29`

Step 3 : Substituting this value of y in Equation (3), we get

x = 3 – 2 (`19/29` )

x=49

Therefore, the solution is x =`49/29` , y =`19/29`