Solve {l}{A=x-2y+3}{B=4x+5y-6}{x=3}{y=2}{a=3A-B}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { A = x - 2 y + 3 }\\ { B = 4 x + 5 y - 6 }\\ { x = 3 }\\ { y = 2 }\\ { a = 3 A - B }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for A, x, y, B, a, b

$$b=-10$$

Solution Steps

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

$$A=3-2\times 2+3$$

Multiply -2 and 2 to get -4.

$$A=3-4+3$$

Subtract 4 from 3 to get -1.

$$A=-1+3$$

Add -1 and 3 to get 2.

$$A=2$$

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

$$B=4\times 3+5\times 2-6$$

Do the multiplications.

$$B=12+10-6$$

Add 12 and 10 to get 22.

$$B=22-6$$

Subtract 6 from 22 to get 16.

$$B=16$$

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

$$a=3\times 2-16$$

Do the multiplications.

$$a=6-16$$

Subtract 16 from 6 to get -10.

$$a=-10$$

Consider the equation (6). Insert the known values of variables into the equation.

$$b=-10$$

The system is now solved.

$$A=2 x=3 y=2 B=16 a=-10 b=-10$$