Solve {l}{97*77+13x={(2*97+x)}*33}{y=2}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 97 \cdot 77 + 13 x = {(2 \cdot 97 + x)} \cdot 33 }\\ { y = 2 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=2$$

Solution Steps

Consider the first equation. Multiply 97 and 77 to get 7469.

$$7469+13x=\left(2\times 97+x\right)\times 33$$

Multiply 2 and 97 to get 194.

$$7469+13x=\left(194+x\right)\times 33$$

Use the distributive property to multiply 194+x by 33.

$$7469+13x=6402+33x$$

Subtract 33x from both sides.

$$7469+13x-33x=6402$$

Combine 13x and -33x to get -20x.

$$7469-20x=6402$$

Subtract 7469 from both sides.

$$-20x=6402-7469$$

Subtract 7469 from 6402 to get -1067.

$$-20x=-1067$$

Divide both sides by -20.

$$x=\frac{-1067}{-20}$$

Fraction \frac{-1067}{-20} can be simplified to \frac{1067}{20} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{1067}{20}$$

The system is now solved.

$$x=\frac{1067}{20} y=2 z=2$$