Solve {l}{3x+10=y+5}{5(x+1)=3(x+5)}

$$\left\{ \begin{array} { l } { 3 x + 10 = y + 5 } \\ { 5 ( x + 1 ) = 3 ( x + 5 ) } \end{array} \right.$$

Solve for x, y

$$x=5$$

$$y=20$$

Solution Steps

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

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

Use the distributive property to multiply 3 by x+5.

$$5x+5=3x+15$$

Subtract 3x from both sides.

$$5x+5-3x=15$$

Combine 5x and -3x to get 2x.

$$2x+5=15$$

Subtract 5 from both sides.

$$2x=15-5$$

Subtract 5 from 15 to get 10.

$$2x=10$$

Divide both sides by 2.

$$x=\frac{10}{2}$$

Divide 10 by 2 to get 5.

$$x=5$$

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

$$3\times 5+10=y+5$$

Multiply 3 and 5 to get 15.

$$15+10=y+5$$

Add 15 and 10 to get 25.

$$25=y+5$$

Swap sides so that all variable terms are on the left hand side.

$$y+5=25$$

Subtract 5 from both sides.

$$y=25-5$$

Subtract 5 from 25 to get 20.

$$y=20$$

The system is now solved.

$$x=5 y=20$$