14x+23y=14

The standard form of a linear equation is Ax+By=C.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

4,3,4

Since 4,3,4 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 4,3,4 then find LCM for the variable part .

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

4 has factors of 2 and 2.

2⋅2

Since 3 has no factors besides 1 and 3.

3 is a prime number

4 has factors of 2 and 2.

2⋅2

The LCM of 4,3,4 is the result of multiplying all prime factors the greatest number of times they occur in either number.

2⋅2⋅3

The LCM of 4,3,4 is 2⋅2⋅3=12.

Multiply 2 by 2.

4⋅3

Multiply 4 by 3.

12

12

12

Multiply both sides by 12.

12(14x+23y)=12(14)

Simplify each term.

Combine 14 and x.

12(x4+23y)=12(14)

Combine 23 and y.

12(x4+2y3)=12(14)

12(x4+2y3)=12(14)

Simplify terms.

Apply the distributive property.

12×4+122y3=12(14)

Cancel the common factor of 4.

Factor 4 out of 12.

4(3)x4+122y3=12(14)

Cancel the common factor.

4⋅3×4+122y3=12(14)

Rewrite the expression.

3x+122y3=12(14)

3x+122y3=12(14)

Cancel the common factor of 3.

Factor 3 out of 12.

3x+3(4)2y3=12(14)

Cancel the common factor.

3x+3⋅42y3=12(14)

Rewrite the expression.

3x+4(2y)=12(14)

3x+4(2y)=12(14)

Multiply 2 by 4.

3x+8y=12(14)

3x+8y=12(14)

3x+8y=12(14)

Factor 4 out of 12.

3x+8y=4(3)14

Cancel the common factor.

3x+8y=4⋅314

Rewrite the expression.

3x+8y=3

3x+8y=3

Rewrite in Standard Form 1/4x+2/3y=1/4