Substitution Method (Math Help)

The Substitution method is a method for solving equations with more than one variable. This method is very useful in equations with two variables and is commonly used in solving a pair of linear simultaneous equations. The first equation is solved for one variable in terms of the other and this value is substituted in the second equation. This is illustrated below with examples

Introduction for substitution method variables:

* Substitution method is commonly used to solve a pair of linear simultaneous equations. Linear simultaneous equations can be solved by two methods one is elimination method another one is substitution method.

* Given two equations, solve for one variable from one of the equations and then substitute the value of that variable into the other equation

How to solve by substitution method

1) Solve the two equations using substitution method to find the variable x and y.

3x + 4y = -9

y + 8 = 5x

Solution:

Step 1: First choose an equation where the variable is 1.So choose the equation 2.

y = 5x - 8

Step 2: From the previous equation we know that variable y is same as 5x - 8

3x + 4(5x - 8) = -9

3x + 20x - 32 = -9

Step 3: Combine the terms

23x = 23

X = 1

Step 4: substitute the value x in equation 1

3x+4y=-9

3(1) +4y=-9

3+4y= -9

4y=-9-3

y = -3

The solution is, x = 1 and y = -3

2) Solve for Variables x and y, where, 2x + 2y - 6 = 0 and 3x + y + 4 = 0.

Solution: 2x + 2y - 6 = 0 ? (1)

3x + y + 4 = 0 ? (2)

Let us consider the equation (1) => 2x + 2y - 6 = 0

=> 2y = - 2x + 6

=> y = -x + 3 ? (3)

Now, plug equation (3) in equation (2).

(2) => 3x + y + 4 = 0

=> 3x + (-x + 3) + 4 = 0

=> 3x - x + 3 + 6 = 0

=> 2x + 9 = 0

=> 2x = - 18

=> x = - 9

Now, plug x = -9 in Equation (1).

(1) => 2x + 2y - 6 = 0

=> 2(- 9) + 2y - 6 = 0

=> - 18 + 2y - 6 = 0

=> 2y - 22 = 0

=> y = 11.

The solutions are x = - 9 and y = 11.

3) Solve the equations by using the method of substitution and find the variables x and y.

2x - y = -5

3x+8y =-55

Solution:

Step 1: Rearrange the first equation,
2x - y = -5
y = x + 5

Step 2: Substitute 1st equation on equation 2

3x + 8(2x + 5) = -55

Step 3: Expand and simplify the equation:
3x + 16x + 40 = -55
19x = -95
x = -5

Step 4: Substitute x values in 1st equation

2(-5) - y = -5

-10-y=-5

-5=y

Y=-5

Solution: x = -8, y = -5

Steps to solve substitution method:

Step 1: For solving substitution method to write a variable in terms of another variable.

Step 2: Then substitute that equation in second equation to get a single variable equation.

Step 3: In the next step to solve that single variable equation and then to find the value of that variable.

Step 4: Once we get the value of one variable, substitute that value of variable in any of the equation to get the value of the second variable.

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