Solve {l}{7-3s+1=0}{4t-5s=-17}

$$\left\{ \begin{array} { l } { 7 - 3 s + 1 = 0 } \\ { 4 t - 5 s = - 17 } \end{array} \right.$$

Solve for s, t

$$t=-\frac{11}{12}\approx -0.916666667$$

$$s = \frac{8}{3} = 2\frac{2}{3} \approx 2.666666667$$

Solution Steps

Consider the first equation. Add 7 and 1 to get 8.

$$8-3s=0$$

Subtract 8 from both sides. Anything subtracted from zero gives its negation.

$$-3s=-8$$

Divide both sides by -3.

$$s=\frac{-8}{-3}$$

Fraction \frac{-8}{-3} can be simplified to \frac{8}{3} by removing the negative sign from both the numerator and the denominator.

$$s=\frac{8}{3}$$

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

$$4t-5\times \frac{8}{3}=-17$$

Multiply -5 and \frac{8}{3} to get -\frac{40}{3}.

$$4t-\frac{40}{3}=-17$$

Add \frac{40}{3} to both sides.

$$4t=-17+\frac{40}{3}$$

Add -17 and \frac{40}{3} to get -\frac{11}{3}.

$$4t=-\frac{11}{3}$$

Divide both sides by 4.

$$t=\frac{-\frac{11}{3}}{4}$$

Express \frac{-\frac{11}{3}}{4} as a single fraction.

$$t=\frac{-11}{3\times 4}$$

Multiply 3 and 4 to get 12.

$$t=\frac{-11}{12}$$

Fraction \frac{-11}{12} can be rewritten as -\frac{11}{12} by extracting the negative sign.

$$t=-\frac{11}{12}$$

The system is now solved.

$$s=\frac{8}{3} t=-\frac{11}{12}$$