0.08x-0.01y=4.6

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

Multiply by 100100 to remove the decimal.

100⋅0.08100x-0.01y=4.6

Multiply 100 by 0.08.

8100x-0.01y=4.6

Cancel the common factor of 8 and 100.

Factor 4 out of 8.

4(2)100x-0.01y=4.6

Cancel the common factors.

Factor 4 out of 100.

4⋅24⋅25x-0.01y=4.6

Cancel the common factor.

4⋅24⋅25x-0.01y=4.6

Rewrite the expression.

225x-0.01y=4.6

225x-0.01y=4.6

225x-0.01y=4.6

225x-0.01y=4.6

Multiply by 100100 to remove the decimal.

225x+100⋅-0.01100y=4.6

Multiply 100 by -0.01.

225x+-1100y=4.6

Move the negative in front of the fraction.

225x-1100y=4.6

225x-1100y=4.6

Multiply by 1010 to remove the decimal.

225x-1100y=10⋅4.610

Multiply 10 by 4.6.

225x-1100y=4610

Cancel the common factor of 46 and 10.

Factor 2 out of 46.

225x-1100y=2(23)10

Cancel the common factors.

Factor 2 out of 10.

225x-1100y=2⋅232⋅5

Cancel the common factor.

225x-1100y=2⋅232⋅5

Rewrite the expression.

225x-1100y=235

225x-1100y=235

225x-1100y=235

225x-1100y=235

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

25,100,5

Since 25,100,5 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 25,100,5 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.

25 has factors of 5 and 5.

5⋅5

The prime factors for 100 are 2⋅2⋅5⋅5.

100 has factors of 2 and 50.

2⋅50

50 has factors of 2 and 25.

2⋅2⋅25

25 has factors of 5 and 5.

2⋅2⋅5⋅5

2⋅2⋅5⋅5

Since 5 has no factors besides 1 and 5.

5 is a prime number

The LCM of 25,100,5 is the result of multiplying all prime factors the greatest number of times they occur in either number.

2⋅2⋅5⋅5

The LCM of 25,100,5 is 2⋅2⋅5⋅5=100.

Multiply 2 by 2.

4⋅5⋅5

Multiply 4 by 5.

20⋅5

Multiply 20 by 5.

100

100

100

Multiply both sides by 100.

100(225x-1100y)=100(235)

Simplify each term.

Combine 225 and x.

100(2×25-1100y)=100(235)

Combine y and 1100.

100(2×25-y100)=100(235)

100(2×25-y100)=100(235)

Simplify terms.

Apply the distributive property.

1002×25+100(-y100)=100(235)

Cancel the common factor of 25.

Factor 25 out of 100.

25(4)2×25+100(-y100)=100(235)

Cancel the common factor.

25⋅42×25+100(-y100)=100(235)

Rewrite the expression.

4(2x)+100(-y100)=100(235)

4(2x)+100(-y100)=100(235)

Multiply 2 by 4.

8x+100(-y100)=100(235)

Cancel the common factor of 100.

Move the leading negative in -y100 into the numerator.

8x+100-y100=100(235)

Cancel the common factor.

8x+100-y100=100(235)

Rewrite the expression.

8x-y=100(235)

8x-y=100(235)

8x-y=100(235)

8x-y=100(235)

Cancel the common factor of 5.

Factor 5 out of 100.

8x-y=5(20)235

Cancel the common factor.

8x-y=5⋅20235

Rewrite the expression.

8x-y=20⋅23

8x-y=20⋅23

Multiply 20 by 23.

8x-y=460

8x-y=460

Rewrite in Standard Form 0.08x-0.01y=4.6