15x+12y=145

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.

5,2,5

Since 5,2,5 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 5,2,5 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.

Since 5 has no factors besides 1 and 5.

5 is a prime number

Since 2 has no factors besides 1 and 2.

2 is a prime number

Since 5 has no factors besides 1 and 5.

5 is a prime number

The LCM of 5,2,5 is the result of multiplying all prime factors the greatest number of times they occur in either number.

2⋅5

Multiply 2 by 5.

10

10

Multiply both sides by 10.

10(15x+12y)=10(145)

Simplify each term.

Combine 15 and x.

10(x5+12y)=10(145)

Combine 12 and y.

10(x5+y2)=10(145)

10(x5+y2)=10(145)

Simplify terms.

Apply the distributive property.

10×5+10y2=10(145)

Cancel the common factor of 5.

Factor 5 out of 10.

5(2)x5+10y2=10(145)

Cancel the common factor.

5⋅2×5+10y2=10(145)

Rewrite the expression.

2x+10y2=10(145)

2x+10y2=10(145)

Cancel the common factor of 2.

Factor 2 out of 10.

2x+2(5)y2=10(145)

Cancel the common factor.

2x+2⋅5y2=10(145)

Rewrite the expression.

2x+5y=10(145)

2x+5y=10(145)

2x+5y=10(145)

2x+5y=10(145)

Cancel the common factor of 5.

Factor 5 out of 10.

2x+5y=5(2)145

Cancel the common factor.

2x+5y=5⋅2145

Rewrite the expression.

2x+5y=2⋅14

2x+5y=2⋅14

Multiply 2 by 14.

2x+5y=28

2x+5y=28

Rewrite in Standard Form 1/5x+1/2y=14/5