Solve {l}{5*(x+1)/3=3}{3*(x+1)-y=7}

$$\left\{ \begin{array} { l } { \frac { 5 \cdot ( x + 1 ) } { 3 } = 3 } \\ { 3 \cdot ( x + 1 ) - y = 7 } \end{array} \right.$$

Solve for x, y

$$x=\frac{4}{5}=0.8$$

$$y = -\frac{8}{5} = -1\frac{3}{5} = -1.6$$

Solution Steps

Consider the first equation. Multiply both sides by 3.

$$5\left(x+1\right)=3\times 3$$

Use the distributive property to multiply 5 by x+1.

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

Multiply 3 and 3 to get 9.

$$5x+5=9$$

Subtract 5 from both sides.

$$5x=9-5$$

Subtract 5 from 9 to get 4.

$$5x=4$$

Divide both sides by 5.

$$x=\frac{4}{5}$$

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

$$3\left(\frac{4}{5}+1\right)-y=7$$

Add \frac{4}{5} and 1 to get \frac{9}{5}.

$$3\times \frac{9}{5}-y=7$$

Multiply 3 and \frac{9}{5} to get \frac{27}{5}.

$$\frac{27}{5}-y=7$$

Subtract \frac{27}{5} from both sides.

$$-y=7-\frac{27}{5}$$

Subtract \frac{27}{5} from 7 to get \frac{8}{5}.

$$-y=\frac{8}{5}$$

Divide both sides by -1.

$$y=\frac{\frac{8}{5}}{-1}$$

Express \frac{\frac{8}{5}}{-1} as a single fraction.

$$y=\frac{8}{5\left(-1\right)}$$

Multiply 5 and -1 to get -5.

$$y=\frac{8}{-5}$$

Fraction \frac{8}{-5} can be rewritten as -\frac{8}{5} by extracting the negative sign.

$$y=-\frac{8}{5}$$

The system is now solved.

$$x=\frac{4}{5} y=-\frac{8}{5}$$