Solve {l}{+3y-2=0}{+(k-2)y-5=0}

$$\left. \begin{array} { l } { + 3 y - 2 = 0 } \\ { + ( k - 2 ) y - 5 = 0 } \end{array} \right.$$

Solve for y, k

$$y=\frac{2}{3}\approx 0.666666667$$

$$k = \frac{19}{2} = 9\frac{1}{2} = 9.5$$

Solution Steps

Consider the first equation. Add 2 to both sides. Anything plus zero gives itself.

$$3y=2$$

Divide both sides by 3.

$$y=\frac{2}{3}$$

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

$$\left(k-2\right)\times \frac{2}{3}-5=0$$

Use the distributive property to multiply k-2 by \frac{2}{3}.

$$\frac{2}{3}k-\frac{4}{3}-5=0$$

Subtract 5 from -\frac{4}{3} to get -\frac{19}{3}.

$$\frac{2}{3}k-\frac{19}{3}=0$$

Add \frac{19}{3} to both sides. Anything plus zero gives itself.

$$\frac{2}{3}k=\frac{19}{3}$$

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$k=\frac{19}{3}\times \frac{3}{2}$$

Multiply \frac{19}{3} and \frac{3}{2} to get \frac{19}{2}.

$$k=\frac{19}{2}$$

The system is now solved.

$$y=\frac{2}{3} k=\frac{19}{2}$$