5m - 3n = 19; m
- 6n = -7
Answers
Answer:
Step 1 :
19
Simplify ——
6
Equation at the end of step 1 :
5 3 19
((—•m)+(—•m))-(——•m) = 0
3 2 6
Step 2 :
3
Simplify —
2
Equation at the end of step 2 :
5 3 19m
((— • m) + (— • m)) - ——— = 0
3 2 6
Step 3 :
5
Simplify —
3
Equation at the end of step 3 :
5 3m 19m
((— • m) + ——) - ——— = 0
3 2 6
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 3
The right denominator is : 2
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
3 1 0 1
2 0 1 1
Product of all
Prime Factors 3 2 6
Least Common Multiple:
6
Calculating Multipliers :
4.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 2
Right_M = L.C.M / R_Deno = 3
Making Equivalent Fractions :
4.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 5m • 2
—————————————————— = ——————
L.C.M 6
R. Mult. • R. Num. 3m • 3
—————————————————— = ——————
L.C.M 6
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
5m • 2 + 3m • 3 19m
——————————————— = ———
6 6
Equation at the end of step 4 :
19m 19m
——— - ——— = 0
6 6
Step 5 :
Adding fractions which have a common denominator :
5.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
19m - (19m) 0
——————————— = —
6 6
Equation at the end of step 5 :
0 = 0
Step 6 :
Equations which are always true :
6.1 Solve 0 = 0This equation is a tautology (Something which is always true)
Step-by-step explanation:
Answer:
5m – 3n = 19 .....(I)
m – 6n = –7 .....(II)
Multiplying (I) with 2 we get
10m – 6n = 38 .....(III)
m – 6n = –7 .....(IV)
Subtracting (IV) from (III) we get
10m-m-6n-(-6n)=38-(-7)
⇒9m=45
⇒m=45/9
=5
Putting the value of m = 5 in (II) we get
5-6n=-7⇒-6n=-7-5
⇒-6n=-12
⇒n=-12/-6
=2
Thus, (m, n) = (5, 2).