Solve 72/440=frac{20k_{1}+k_{2}}{60k_{11}+10k_{2}}

$$\frac { 72 } { 440 } = \frac { 20 k _ { 1 } + k _ { 2 } } { 60 k _ { 11 } + 10 k _ { 2 } }$$

Solve for k_1

$$k_{1}=\frac{7k_{2}}{220}+\frac{27k_{11}}{55}$$

$$k_{2}\neq -6k_{11}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 440\left(k_{2}+6k_{11}\right), the least common multiple of 440,60k_{11}+10k_{2}.

$$\left(k_{2}+6k_{11}\right)\times 72=44\left(20k_{1}+k_{2}\right)$$

Use the distributive property to multiply k_{2}+6k_{11} by 72.

$$72k_{2}+432k_{11}=44\left(20k_{1}+k_{2}\right)$$

Use the distributive property to multiply 44 by 20k_{1}+k_{2}.

$$72k_{2}+432k_{11}=880k_{1}+44k_{2}$$

Swap sides so that all variable terms are on the left hand side.

$$880k_{1}+44k_{2}=72k_{2}+432k_{11}$$

Subtract 44k_{2} from both sides.

$$880k_{1}=72k_{2}+432k_{11}-44k_{2}$$

Combine 72k_{2} and -44k_{2} to get 28k_{2}.

$$880k_{1}=28k_{2}+432k_{11}$$

Divide both sides by 880.

$$\frac{880k_{1}}{880}=\frac{28k_{2}+432k_{11}}{880}$$

Dividing by 880 undoes the multiplication by 880.

$$k_{1}=\frac{28k_{2}+432k_{11}}{880}$$

Divide 28k_{2}+432k_{11} by 880.

$$k_{1}=\frac{7k_{2}}{220}+\frac{27k_{11}}{55}$$

Solve for k_11

$$k_{11}=\frac{55k_{1}}{27}-\frac{7k_{2}}{108}$$

$$k_{1}\neq -\frac{k_{2}}{20}$$