Solve {l}{2*33(6a+6)=22}{2*33(20a+b)=24}

$$\left\{ \begin{array} { l } { 2 \times 33 ( 6 a + 6 ) = 22 } \\ { 2 \times 33 ( 20 a + b ) = 24 } \end{array} \right.$$

Solve for a, b

$$a=-\frac{17}{18}\approx -0.944444444$$

$$b = \frac{1906}{99} = 19\frac{25}{99} \approx 19.252525253$$

Steps Using Substitution

Consider the first equation. Use the distributive property to multiply 2\times 33 by 6a+6.

$$6\left(2\times 33\right)a+6\left(2\times 33\right)=22$$

Subtract 6\left(2\times 33\right) from both sides.

$$6\left(2\times 33\right)a=22-6\left(2\times 33\right)$$

Consider the second equation. Use the distributive property to multiply 2\times 33 by 20a+b.

$$20\left(2\times 33\right)a+2\times 33b=24$$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$$396a=-374,1320a+66b=24$$

Pick one of the two equations which is more simple to solve for a by isolating a on the left hand side of the equal sign.

$$396a=-374$$

Divide both sides by 396.

$$a=-\frac{17}{18}$$

Substitute -\frac{17}{18} for a in the other equation, 1320a+66b=24.

$$1320\left(-\frac{17}{18}\right)+66b=24$$

Multiply 1320 times -\frac{17}{18}.

$$-\frac{3740}{3}+66b=24$$

Add \frac{3740}{3} to both sides of the equation.

$$66b=\frac{3812}{3}$$

Divide both sides by 66.

$$b=\frac{1906}{99}$$

The system is now solved.

$$a=-\frac{17}{18},b=\frac{1906}{99}$$