Solve {l}{3(2x-1)=-2(x+3)(R)}{5x-3(x+2)=15(R:21/)}

$$\left. \begin{array} { l } { 3 ( 2 x - 1 ) = - 2 ( x + 3 ) ( R ) } \\ { 5 x - 3 ( x + 2 ) = 15 ( R : 21 / ) } \end{array} \right.$$

Solve for x, R

$$x = \frac{21}{2} = 10\frac{1}{2} = 10.5$$

$$R = -\frac{20}{9} = -2\frac{2}{9} \approx -2.222222222$$

Solution Steps

Consider the second equation. Use the distributive property to multiply -3 by x+2.

$$5x-3x-6=15$$

Combine 5x and -3x to get 2x.

$$2x-6=15$$

Add 6 to both sides.

$$2x=15+6$$

Add 15 and 6 to get 21.

$$2x=21$$

Divide both sides by 2.

$$x=\frac{21}{2}$$

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

$$3\left(2\times \frac{21}{2}-1\right)=-2\left(\frac{21}{2}+3\right)R$$

Multiply 2 and \frac{21}{2} to get 21.

$$3\left(21-1\right)=-2\left(\frac{21}{2}+3\right)R$$

Subtract 1 from 21 to get 20.

$$3\times 20=-2\left(\frac{21}{2}+3\right)R$$

Multiply 3 and 20 to get 60.

$$60=-2\left(\frac{21}{2}+3\right)R$$

Add \frac{21}{2} and 3 to get \frac{27}{2}.

$$60=-2\times \frac{27}{2}R$$

Multiply -2 and \frac{27}{2} to get -27.

$$60=-27R$$

Swap sides so that all variable terms are on the left hand side.

$$-27R=60$$

Divide both sides by -27.

$$R=\frac{60}{-27}$$

Reduce the fraction \frac{60}{-27} to lowest terms by extracting and canceling out 3.

$$R=-\frac{20}{9}$$

The system is now solved.

$$x=\frac{21}{2} R=-\frac{20}{9}$$