110x+13y=56
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.
10,3,6
Since 10,3,6 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 10,3,6 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.
10 has factors of 2 and 5.
2⋅5
Since 3 has no factors besides 1 and 3.
3 is a prime number
6 has factors of 2 and 3.
2⋅3
The LCM of 10,3,6 is the result of multiplying all prime factors the greatest number of times they occur in either number.
2⋅3⋅5
The LCM of 10,3,6 is 2⋅3⋅5=30.
Multiply 2 by 3.
6⋅5
Multiply 6 by 5.
30
30
30
Multiply both sides by 30.
30(110x+13y)=30(56)
Simplify each term.
Combine 110 and x.
30(x10+13y)=30(56)
Combine 13 and y.
30(x10+y3)=30(56)
30(x10+y3)=30(56)
Simplify terms.
Apply the distributive property.
30×10+30y3=30(56)
Cancel the common factor of 10.
Factor 10 out of 30.
10(3)x10+30y3=30(56)
Cancel the common factor.
10⋅3×10+30y3=30(56)
Rewrite the expression.
3x+30y3=30(56)
3x+30y3=30(56)
Cancel the common factor of 3.
Factor 3 out of 30.
3x+3(10)y3=30(56)
Cancel the common factor.
3x+3⋅10y3=30(56)
Rewrite the expression.
3x+10y=30(56)
3x+10y=30(56)
3x+10y=30(56)
3x+10y=30(56)
Cancel the common factor of 6.
Factor 6 out of 30.
3x+10y=6(5)56
Cancel the common factor.
3x+10y=6⋅556
Rewrite the expression.
3x+10y=5⋅5
3x+10y=5⋅5
Multiply 5 by 5.
3x+10y=25
3x+10y=25
Rewrite in Standard Form 1/10x+1/3y=5/6
