Solve {l}{4y-2=7}{y-3z=10}

$$\left. \begin{array} { l } { 4 y - 2 = 7 } \\ { y - 3 z = 10 } \end{array} \right.$$

Solve for y, z

$$y = \frac{9}{4} = 2\frac{1}{4} = 2.25$$

$$z = -\frac{31}{12} = -2\frac{7}{12} \approx -2.583333333$$

Solution Steps

Consider the first equation. Add 2 to both sides.

$$4y=7+2$$

Add 7 and 2 to get 9.

$$4y=9$$

Divide both sides by 4.

$$y=\frac{9}{4}$$

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

$$\frac{9}{4}-3z=10$$

Subtract \frac{9}{4} from both sides.

$$-3z=10-\frac{9}{4}$$

Subtract \frac{9}{4} from 10 to get \frac{31}{4}.

$$-3z=\frac{31}{4}$$

Divide both sides by -3.

$$z=\frac{\frac{31}{4}}{-3}$$

Express \frac{\frac{31}{4}}{-3} as a single fraction.

$$z=\frac{31}{4\left(-3\right)}$$

Multiply 4 and -3 to get -12.

$$z=\frac{31}{-12}$$

Fraction \frac{31}{-12} can be rewritten as -\frac{31}{12} by extracting the negative sign.

$$z=-\frac{31}{12}$$

The system is now solved.

$$y=\frac{9}{4} z=-\frac{31}{12}$$