STEEMIT MATH CLASS | LESSON 3 - SOLVING LINEAR EQUATIONS BY SUBSTITUTION METHOD.

Hello Everyone, you are welcome to Steemit Math Class with @whileponderin. In the last class, we explained what a linear equation is, as well as it's properties. We also talked about how to add and subtract algebra, how to solve linear equations with one variable and also how to plot a linear equation with one or two variables in a graph.

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Just as promised, in today's lesson, we will be discussing how to solve linear equations with two variables using the substitution method. If you haven't read the last class, you can read about it here Lesson 2: Linear Equation

SOLVING LINEAR EQUATIONS BY SUBSTITUTION METHOD

One of the methods of solving two linear equations with 2 variables, is by substituting one of the equations into the other equation. This can be done by rearranging the equation, making one of the variables in one of the equations the subject of formulae. Then we will replace that same variable in the second with the equivalent of that variable as obtained from the first equation. Now, I know this explanation is a bit confusing, let me explain it better with the aid of an example.

Example 1: Given two linear equations

x + y = 6 --------------(1)
2x + 4y = 20 -----------(2)

Find the values for x and y.

CASE SCENARIO 1

Step 1: Pick any of the equations, and make one of their variables the subject of formular.

In the example above, we have two equations, x + y = 6 and 2x + 4y = 20. These equations have two variables "x" and "y". We can decide to pick the equation x + y = 6, and we then make "x" the subject of formula.

making "x" subject of formular, we will obtain

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

Step 2: Substitute the variable you made a subject of formular with the new equation you obtained.

The second equation is

2x + 4y = 20

The variable we made subject of formulae was "x". When we did, we obtained the equation (3).

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

Substituting this, we will obtain:

2(6 - y) + 4y = 20 ------- (4)

Step 3: Solving the newly formed equation,

12 - 2y + 4y = 20

2y = 20 - 12.

2y = 8.

y = 8/2 = 4.

Step 4: Having obtained the value of y as 4, we can obtain the value of "x" by substituting "y" in any of the equations above, with the value (4) we obtained above.

Let's say we pick the first equation

x + (y) = 6

Replacing y = 4

x + 4 = 6

Thus, x = 6 - 4 = 2.
Therefore x = 2.

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Assuming we pick the second equation, we would have obtained the same result. This is shown below.

Let's say we pick the second equation

2x + 4y = 20

Remember that we obtained y = 4

Replacing y = 4 in the equation above, we will obtain

2x + 4(4) = 20

2x + 16 = 20.

2x = 20 - 16.

2x = 4.

x = 4/2 = 2.

Therefore x = 2.

You can see that the value for x is the same regardless of which of the equations you substituted it into.

CASE SCENARIO 2

One may ask, assuming that we picked the second equation and made one of the variables their the subject of variable, would we get the same result?

Let's say we pick 2x + 4y = 20 and make y the subject of equation. To do that,

2x + 4y = 20.

4y = 20 - 2x

y = (20 - 2x)/4 ------- (5)

As we did in the first Scenario, we will replace the variable "y" in the other equation given.

x + y = 6.

Replacing "y" in the equation. With the new equation for y derived,

x + ((20 - 2x)/4) = 6

Resolving this, and removing the denominator in the equation. We multiply all part of the equation with the denominator (4).

4x + 20 - 2x = 24

Collecting like terms,

4x - 2x = 24 - 20.

2x = 4

x = 4/2

x = 2.

Having obtained the value of "x" as 2, we can obtain the value of "y" by substituting "x" in any of the equations above, with the value (2) we obtained above.

Let's say we pick the first equation

x + y = 6.

We obtained the value of x to be 2. Substituting it to one of the equations we we are solving for,

(2) + y = 6.

Collecting like terms.

y = 6 - 2

y = 4

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Assuming we pick the second equation, we would have obtained the same result. This is shown below.

Let's say we pick the second equation

2(x) + 4y = 20

Remember that we obtained x = 2

2(2) + 4y = 20

4 + 4y = 20.

Collecting like terms,

4y = 20 - 4.

y = 16/4

y = 4.

Thus, x = 2, y = 4.

You can see that regardless of which you equation or variable you chose, the results you will obtain, should be the same.

CHECKING YOUR ANSWERS

After solving a two variable linear equation, you can check your answer by substituting the values for "x" and "y" you obtained into any of the equations to know if you will obtain the same result.

a. x + y = 6.

Substituting x = 2, y = 4

2 + 4 = 6

6 = 6.

This shows that our answer is correct.

b. 2(x) + 4(y) = 20

x = 2, y = 4

2(2) + 4 (4) = 20

4 + 16 = 20.

20 = 20.

SUMMARY

In this post, we have been able, to explain how to solve linear equations with two variables using the substitution method. We have been able to show that regardless of which of the equations or the variables you choose you will arrive at the same answer. At the end of the class, we were showed how to check if the solutions we obtained are correct.

In the coming sub-lessons, we will be discussing how to solve linear equations with two variables using other methods such as, graphical method, the cross multiplication method, the determinant method, and the elimination method. So, stay tuned to this blog. To check your progress for this lesson, try out these activities.

ACTIVITY

1. Solve the following linear equations using substitution method:

x+y=7 ------- (1)
x-y=8 ------- (2)

Pick the first equation and make "x" the subject of formula while solving.

2. Solve the same linear equations given in question 1 again, but this time, pick the second equation and make "y" the subject of formula while solving..

3. Check if your values for "x" and "y" are correct by using the method taught in the class.

INTERESTING SCIENCE FACT: Did You know that ...

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I hope you found this lesson informative. Till next time

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