Solve {l}{0,5-3,4(5-y)=4,7}{-4x+8y=12}

$$\left\{ \begin{array} { l } { 0,5 - 3,4 ( 5 - y ) = 4,7 } \\ { - 4 x + 8 y = 12 } \end{array} \right.$$

Solve for y, x

$$x=\frac{161}{17}\approx 9,470588235$$

$$y=\frac{106}{17}\approx 6,235294118$$

Solution Steps

Consider the first equation. Use the distributive property to multiply -3,4 by 5-y.

$$0,5-17+3,4y=4,7$$

Subtract 17 from 0,5 to get -16,5.

$$-16,5+3,4y=4,7$$

Add 16,5 to both sides.

$$3,4y=4,7+16,5$$

Add 4,7 and 16,5 to get 21,2.

$$3,4y=21,2$$

Divide both sides by 3,4.

$$y=\frac{21,2}{3,4}$$

Expand \frac{21,2}{3,4} by multiplying both numerator and the denominator by 10.

$$y=\frac{212}{34}$$

Reduce the fraction \frac{212}{34} to lowest terms by extracting and canceling out 2.

$$y=\frac{106}{17}$$

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

$$-4x+8\times \frac{106}{17}=12$$

Multiply 8 and \frac{106}{17} to get \frac{848}{17}.

$$-4x+\frac{848}{17}=12$$

Subtract \frac{848}{17} from both sides.

$$-4x=12-\frac{848}{17}$$

Subtract \frac{848}{17} from 12 to get -\frac{644}{17}.

$$-4x=-\frac{644}{17}$$

Divide both sides by -4.

$$x=\frac{-\frac{644}{17}}{-4}$$

Express \frac{-\frac{644}{17}}{-4} as a single fraction.

$$x=\frac{-644}{17\left(-4\right)}$$

Multiply 17 and -4 to get -68.

$$x=\frac{-644}{-68}$$

Reduce the fraction \frac{-644}{-68} to lowest terms by extracting and canceling out -4.

$$x=\frac{161}{17}$$

The system is now solved.

$$y=\frac{106}{17} x=\frac{161}{17}$$