Solve {l}{x-2/2-x-3/4=x-4/5}{y=3x*102x}{z=y}{a=z}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { \frac{x - 2}{2} - \frac{x - 3}{4} = \frac{x - 4}{5} }\\ { y = 3 x \cdot 102 x }\\ { z = y }\\ { a = z }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for x, y, z, a, b

$$b=37026$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 20, the least common multiple of 2,4,5.

$$10\left(x-2\right)-5\left(x-3\right)=4\left(x-4\right)$$

Use the distributive property to multiply 10 by x-2.

$$10x-20-5\left(x-3\right)=4\left(x-4\right)$$

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

$$10x-20-5x+15=4\left(x-4\right)$$

Combine 10x and -5x to get 5x.

$$5x-20+15=4\left(x-4\right)$$

Add -20 and 15 to get -5.

$$5x-5=4\left(x-4\right)$$

Use the distributive property to multiply 4 by x-4.

$$5x-5=4x-16$$

Subtract 4x from both sides.

$$5x-5-4x=-16$$

Combine 5x and -4x to get x.

$$x-5=-16$$

Add 5 to both sides.

$$x=-16+5$$

Add -16 and 5 to get -11.

$$x=-11$$

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

$$y=3\left(-11\right)\times 102\left(-11\right)$$

Multiply 3 and -11 to get -33.

$$y=-33\times 102\left(-11\right)$$

Multiply -33 and 102 to get -3366.

$$y=-3366\left(-11\right)$$

Multiply -3366 and -11 to get 37026.

$$y=37026$$

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

$$z=37026$$

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

$$a=37026$$

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

$$b=37026$$

The system is now solved.

$$x=-11 y=37026 z=37026 a=37026 b=37026$$