Solve {l}{7n+2/4=8-3n/5}{7(x+1)/9-13=2x}

$$\left. \begin{array} { l } { \frac { 7 n + 2 } { 4 } = \frac { 8 - 3 n } { 5 } } \\ { \frac { 7 ( x + 1 ) } { 9 } - 13 = 2 x } \end{array} \right.$$

Solve for n, x

$$x=-10$$

$$n=\frac{22}{47}\approx 0.468085106$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 20, the least common multiple of 4,5.

$$5\left(7n+2\right)=4\left(8-3n\right)$$

Use the distributive property to multiply 5 by 7n+2.

$$35n+10=4\left(8-3n\right)$$

Use the distributive property to multiply 4 by 8-3n.

$$35n+10=32-12n$$

Add 12n to both sides.

$$35n+10+12n=32$$

Combine 35n and 12n to get 47n.

$$47n+10=32$$

Subtract 10 from both sides.

$$47n=32-10$$

Subtract 10 from 32 to get 22.

$$47n=22$$

Divide both sides by 47.

$$n=\frac{22}{47}$$

Consider the second equation. Multiply both sides of the equation by 9.

$$7\left(x+1\right)-117=18x$$

Use the distributive property to multiply 7 by x+1.

$$7x+7-117=18x$$

Subtract 117 from 7 to get -110.

$$7x-110=18x$$

Subtract 18x from both sides.

$$7x-110-18x=0$$

Combine 7x and -18x to get -11x.

$$-11x-110=0$$

Add 110 to both sides. Anything plus zero gives itself.

$$-11x=110$$

Divide both sides by -11.

$$x=\frac{110}{-11}$$

Divide 110 by -11 to get -10.

$$x=-10$$

The system is now solved.

$$n=\frac{22}{47} x=-10$$