Homework post by @dorismos || LESSON 3 - Solving linear equations by substitution method || 21-7-22

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Greetings to everyone in this community. I'm @dorismos and this is going to be my first homework post on mathematics. Before I begin, I'll love to commend and render my appreciation to @whileponderin for the time taken to draft out and analyze solving linear equations simultaneous method/equation.

The way you made it clear and understandable using more than one methods to solve and then to confirm the answers is worth appreciating. Since this week is on Solving linear equations using simultaneous method/equation, I'll love to do justice to the homework given accordingly. The way you made this easy and understandable reminds me of my mathematics tutor who defined maths as shown below...

M: My friends are few
A: Accountants can't do without me
T: Teachers have their own way of solving me
H: Handle me with care
S: Solve me in any examination without using micro chips or involving in examination malpractice.

Anyways, below are the questions given me. And I'll take the first one.

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

Question 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.

Solution

Make x subject in equation one. This can be done by taking y to the right hand side to meet 7 so that x can stand alone.

x + y =7 -------------- 1

Once y crosses to the other side, the side changes to negative which is a common rule when collecting like terms on when solving equations.

x = 7- y
x =7 - y ----------- 3

Now, substituting what you have as the value of x in equation 3 into equation 2, we have,

x-y=8

7 - y - y= 8

7 - 2y = 8

Collect like terms:

We'll take 7 which has an invisible positive sign in front of it to the right hand side to meet 8. When 7 crosses, it becomes negative.

-2y = 8 -7
-2y = 1

Divide both sides by -2

-2y/-2 = -1/2

y= -1/2
y= -0.5

Now you've found the value of y
Substitute the value of y being -0.5 in equation 1 x+y=7

x - 0.5 = 7

Collect like terms. In collecting like terms, -0.5 will cross to meet 7 and as it crosses, the sign changes from negative to positive..

x = 7+0.5

x = 7.5

Therefore, the value of x = 7.5 and y =- 0.5

Question 2

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

Solution

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

Making y subject of the formula, we have
x - y = 8

To make y subject, you take x to the other side. You'll have,

• y = 8-x

Divide both sides by -1

-y/-1 = 8 - x/-1

y = -8-x

Substituting -8-x for y in equation 1

x+(-8-x)=7

x-8-x=7

2x=7+8
2x= 15

Divide both sides by 2 to make x subject..
2x/2=15/2
x= 7.5

Substituting 7.5 for x into equation 2 (x-y=8)

7.5 - y= 8
-y=8-7.5
-y= 0.5

Divide both sides by -1

-y/-1 = 0.5/-1

y = -0.5

Question 3

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

Equation 1: x+y=7

If x=7.5 and y=-0.5, then

7.5+(-0.5)= 7
7.5 - 0.5 = 7

The solution is very correct....For equation 2,

Equation 2: x-y=8

If x=7.5 and y=-0.5

7.5-(-0.5)=8
7.5 + 0.5 = 8

The solution is very correct.

Cc,
@ngoenyi
@steemkidss
@patjewell