Solve {l}{4r-3s=2}{2+1s=6}

$$\left. \begin{array} { l } { 4 r - 3 s = 2 } \\ { 2 + 1 s = 6 } \end{array} \right.$$

Solve for r, s

$$r = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

$$s=4$$

Solution Steps

Consider the second equation. Subtract 2 from both sides.

$$1s=6-2$$

Subtract 2 from 6 to get 4.

$$1s=4$$

Divide both sides by 1.

$$s=4$$

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

$$4r-3\times 4=2$$

Multiply -3 and 4 to get -12.

$$4r-12=2$$

Add 12 to both sides.

$$4r=2+12$$

Add 2 and 12 to get 14.

$$4r=14$$

Divide both sides by 4.

$$r=\frac{14}{4}$$

Reduce the fraction \frac{14}{4} to lowest terms by extracting and canceling out 2.

$$r=\frac{7}{2}$$

The system is now solved.

$$r=\frac{7}{2} s=4$$