Solve {l}{35/a=7/2}{x/6=22/44}{frac{15}{45}=frac{9}{y}}{frac{z}{5}=frac{20}{25}}

$$\left. \begin{array} { l } { \frac { 35 } { a } = \frac { 7 } { 2 } } \\ { \frac { x } { 6 } = \frac { 22 } { 44 } } \\ { \frac { 15 } { 45 } = \frac { 9 } { y } } \\ { \frac { z } { 5 } = \frac { 20 } { 25 } } \end{array} \right.$$

Solve for a, x, y, z

$$x=3$$

$$y=27$$

$$z=4$$

$$a=10$$

Solution Steps

Consider the first equation. Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2a, the least common multiple of a,2.

$$2\times 35=7a$$

Multiply 2 and 35 to get 70.

$$70=7a$$

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

$$7a=70$$

Divide both sides by 7.

$$a=\frac{70}{7}$$

Divide 70 by 7 to get 10.

$$a=10$$

Consider the second equation. Multiply both sides of the equation by 132, the least common multiple of 6,44.

$$22x=3\times 22$$

Multiply 3 and 22 to get 66.

$$22x=66$$

Divide both sides by 22.

$$x=\frac{66}{22}$$

Divide 66 by 22 to get 3.

$$x=3$$

Consider the third equation. Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 45y, the least common multiple of 45,y.

$$y\times 15=45\times 9$$

Multiply 45 and 9 to get 405.

$$y\times 15=405$$

Divide both sides by 15.

$$y=\frac{405}{15}$$

Divide 405 by 15 to get 27.

$$y=27$$

Consider the fourth equation. Multiply both sides of the equation by 25, the least common multiple of 5,25.

$$5z=20$$

Divide both sides by 5.

$$z=\frac{20}{5}$$

Divide 20 by 5 to get 4.

$$z=4$$

The system is now solved.

$$a=10 x=3 y=27 z=4$$