Solve {l}{3x+5=0}{5y+x=10}

$$\left\{ \begin{array} { l } { 3 x + 5 = 0 } \\ { 5 y + x = 10 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1.666666667$$

$$y = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

Solution Steps

Consider the first equation. Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$3x=-5$$

Divide both sides by 3.

$$x=-\frac{5}{3}$$

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

$$5y-\frac{5}{3}=10$$

Add \frac{5}{3} to both sides.

$$5y=10+\frac{5}{3}$$

Add 10 and \frac{5}{3} to get \frac{35}{3}.

$$5y=\frac{35}{3}$$

Divide both sides by 5.

$$y=\frac{\frac{35}{3}}{5}$$

Express \frac{\frac{35}{3}}{5} as a single fraction.

$$y=\frac{35}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$y=\frac{35}{15}$$

Reduce the fraction \frac{35}{15} to lowest terms by extracting and canceling out 5.

$$y=\frac{7}{3}$$

The system is now solved.

$$x=-\frac{5}{3} y=\frac{7}{3}$$