Solve {l}{2/x+3/y=2}{4/y-9/y+1=0}

$$\left. \begin{array} { l } { \frac { 2 } { x } + \frac { 3 } { y } = 2 } \\ { \frac { 4 } { y } - \frac { 9 } { y } + 1 = 0 } \end{array} \right.$$

Solve for x, y

$$x = \frac{10}{7} = 1\frac{3}{7} \approx 1.428571429$$

$$y=5$$

Solution Steps

Consider the second equation. Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$4-9+y=0$$

Subtract 9 from 4 to get -5.

$$-5+y=0$$

Add 5 to both sides. Anything plus zero gives itself.

$$y=5$$

Consider the first equation. Insert the known values of variables into the equation.

$$\frac{2}{x}+\frac{3}{5}=2$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5x, the least common multiple of x,5.

$$5\times 2+x\times 3=10x$$

Multiply 5 and 2 to get 10.

$$10+x\times 3=10x$$

Subtract 10x from both sides.

$$10+x\times 3-10x=0$$

Combine x\times 3 and -10x to get -7x.

$$10-7x=0$$

Subtract 10 from both sides. Anything subtracted from zero gives its negation.

$$-7x=-10$$

Divide both sides by -7.

$$x=\frac{-10}{-7}$$

Fraction \frac{-10}{-7} can be simplified to \frac{10}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{10}{7}$$

The system is now solved.

$$x=\frac{10}{7} y=5$$