Solve {l}{6x=30}{2y+2x=20}{4z+y=13}{a=x+yz}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { 6 x = 30 }\\ { 2 y + 2 x = 20 }\\ { 4 z + y = 13 }\\ { a = x + y z }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for x, y, z, a, b

$$b=15$$

Solution Steps

Consider the first equation. Divide both sides by 6.

$$x=\frac{30}{6}$$

Divide 30 by 6 to get 5.

$$x=5$$

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

$$2y+2\times 5=20$$

Multiply 2 and 5 to get 10.

$$2y+10=20$$

Subtract 10 from both sides.

$$2y=20-10$$

Subtract 10 from 20 to get 10.

$$2y=10$$

Divide both sides by 2.

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

Divide 10 by 2 to get 5.

$$y=5$$

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

$$4z+5=13$$

Subtract 5 from both sides.

$$4z=13-5$$

Subtract 5 from 13 to get 8.

$$4z=8$$

Divide both sides by 4.

$$z=\frac{8}{4}$$

Divide 8 by 4 to get 2.

$$z=2$$

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

$$a=5+5\times 2$$

Multiply 5 and 2 to get 10.

$$a=5+10$$

Add 5 and 10 to get 15.

$$a=15$$

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

$$b=15$$

The system is now solved.

$$x=5 y=5 z=2 a=15 b=15$$