Solve {l}{3s+5l=410}{3s+5*(s+26)=410}

$$\left. \begin{array}{l}{ 3 s + 5 l = 410 }\\{ 3 s + 5 \cdot ( s + 26 ) = 410 }\end{array} \right.$$

Solve for s, l

$$s=35$$

$$l=61$$

Solution Steps

Consider the second equation. Use the distributive property to multiply 5 by s+26.

$$3s+5s+130=410$$

Combine 3s and 5s to get 8s.

$$8s+130=410$$

Subtract 130 from both sides.

$$8s=410-130$$

Subtract 130 from 410 to get 280.

$$8s=280$$

Divide both sides by 8.

$$s=\frac{280}{8}$$

Divide 280 by 8 to get 35.

$$s=35$$

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

$$3\times 35+5l=410$$

Multiply 3 and 35 to get 105.

$$105+5l=410$$

Subtract 105 from both sides.

$$5l=410-105$$

Subtract 105 from 410 to get 305.

$$5l=305$$

Divide both sides by 5.

$$l=\frac{305}{5}$$

Divide 305 by 5 to get 61.

$$l=61$$

The system is now solved.

$$s=35 l=61$$