Explained by Ben Lozar

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Basic Algebra. Explained by Ben Lozar. Finding X. 2 Variables. Finding X. Equation: 7x+5=26 Question: What is ‘x’? Answer: x = 3 How do you actually find x = 3? . What is ‘X’? 7x + 5 =26. First. Subtract 5 from both sides. 7x+5-5=26-5 7x = 21. Second. Divide by 7 on both sides

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Basic Algebra

### Explained by Ben Lozar

Finding X

2 Variables

Finding X
• Equation:7x+5=26
• Question:What is ‘x’?
• How do you actually find x = 3?
What is ‘X’? 7x + 5 =26

First

Subtract 5 from both sides.

7x+5-5=26-5

7x = 21

Second

Divide by 7 on both sides

7x/7 = 21/7

Result: x =3

Action

Action

Result

Two Variables
• Two Equations:

2x – 3y = 3

x – y = 5

• How do we solve this?
• 2 ways: Elimination or Substitution
Elimination

First Action

Multiply 1 or both equations to create opposite coefficients

5x – 3y = 3

-3(x – y) = -3(5)

5x – 3y = 3

-3x + 3y = -15

Add both equations together to ELIMINATE one variable and one equation

2x = -12

Something Familiar

Find x

2x/2 = -12/2

X = -6

Then, Substitute x into one of the equations to find y.

-6 –y = 5

-11 = y

X = 6

Y = -11

The Home Stretch

Result

Second Action

2

Substitution

First Step

Something familiar…again!

Solve for the remaining variable

7 = 5y

7/5 = y

Solve for the second variable by substituting the already solved variable

x = 5 – 7/5

x= 12/5

x = 12/5

y = 7/5

Solve 1 equation for either variable

x = 5 – y

Substitute what you got into the other equation

2(5-y) – 3y= 3

10 – 2y – 3y = 3

10 – 5y = 3

Second Step

The Home Stretch