Solve {l}{3(x+y)-5(x-y)=16}{7(y+4)+(y-y)=15}

$$\left\{ \begin{array} { l } { 3 ( x + y ) - 5 ( x - y ) = 16 } \\ { 7 ( y + 4 ) + ( y - y ) = 15 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{108}{7} = -15\frac{3}{7} \approx -15.428571429$$

$$y = -\frac{13}{7} = -1\frac{6}{7} \approx -1.857142857$$

Solution Steps

Consider the second equation. Use the distributive property to multiply 7 by y+4.

$$7y+28+y-y=15$$

Combine 7y and y to get 8y.

$$8y+28-y=15$$

Combine 8y and -y to get 7y.

$$7y+28=15$$

Subtract 28 from both sides.

$$7y=15-28$$

Subtract 28 from 15 to get -13.

$$7y=-13$$

Divide both sides by 7.

$$y=-\frac{13}{7}$$

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

$$3\left(x-\frac{13}{7}\right)-5\left(x-\left(-\frac{13}{7}\right)\right)=16$$

Use the distributive property to multiply 3 by x-\frac{13}{7}.

$$3x-\frac{39}{7}-5\left(x-\left(-\frac{13}{7}\right)\right)=16$$

Multiply -1 and -\frac{13}{7} to get \frac{13}{7}.

$$3x-\frac{39}{7}-5\left(x+\frac{13}{7}\right)=16$$

Use the distributive property to multiply -5 by x+\frac{13}{7}.

$$3x-\frac{39}{7}-5x-\frac{65}{7}=16$$

Combine 3x and -5x to get -2x.

$$-2x-\frac{39}{7}-\frac{65}{7}=16$$

Subtract \frac{65}{7} from -\frac{39}{7} to get -\frac{104}{7}.

$$-2x-\frac{104}{7}=16$$

Add \frac{104}{7} to both sides.

$$-2x=16+\frac{104}{7}$$

Add 16 and \frac{104}{7} to get \frac{216}{7}.

$$-2x=\frac{216}{7}$$

Divide both sides by -2.

$$x=\frac{\frac{216}{7}}{-2}$$

Express \frac{\frac{216}{7}}{-2} as a single fraction.

$$x=\frac{216}{7\left(-2\right)}$$

Multiply 7 and -2 to get -14.

$$x=\frac{216}{-14}$$

Reduce the fraction \frac{216}{-14} to lowest terms by extracting and canceling out 2.

$$x=-\frac{108}{7}$$

The system is now solved.

$$x=-\frac{108}{7} y=-\frac{13}{7}$$