Solve {l}{text{If}2/x+3/y=13text{and}5/x-4/y=-2,text{then}}{text{thesolutionis}}

$$\left. \begin{array} { l } { \text { If } \frac { 2 } { x } + \frac { 3 } { y } = 13 \text { and } \frac { 5 } { x } - \frac { 4 } { y } = - 2 , \text { then } } \\ { \text { the solution is } } \end{array} \right.$$

Solve for x

$$x=-\frac{2y}{3-13y}$$

$$y\neq 0\text{ and }y\neq \frac{3}{13}$$

Steps for Solving Linear Equation

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

$$y\times 2+x\times 3=13xy$$

Subtract 13xy from both sides.

$$y\times 2+x\times 3-13xy=0$$

Subtract y\times 2 from both sides. Anything subtracted from zero gives its negation.

$$x\times 3-13xy=-y\times 2$$

Multiply -1 and 2 to get -2.

$$x\times 3-13xy=-2y$$

Combine all terms containing x.

$$\left(3-13y\right)x=-2y$$

Divide both sides by 3-13y.

$$\frac{\left(3-13y\right)x}{3-13y}=-\frac{2y}{3-13y}$$

Dividing by 3-13y undoes the multiplication by 3-13y.

$$x=-\frac{2y}{3-13y}$$

Variable x cannot be equal to 0.

$$x=-\frac{2y}{3-13y}\text{, }x\neq 0$$