Solve {l}{2x-1/5+34-2/4=2}{3x+1/2-3y+2/4=0}

$$\left\{ \begin{array} { l } { \frac { 2 x - 1 } { 5 } + \frac { 34 - 2 } { 4 } = 2 } \\ { \frac { 3 x + 1 } { 2 } - \frac { 3 y + 2 } { 4 } = 0 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{29}{2} = -14\frac{1}{2} = -14.5$$

$$y=-29$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 20, the least common multiple of 5,4.

$$4\left(2x-1\right)+5\left(34-2\right)=40$$

Use the distributive property to multiply 4 by 2x-1.

$$8x-4+5\left(34-2\right)=40$$

Subtract 2 from 34 to get 32.

$$8x-4+5\times 32=40$$

Multiply 5 and 32 to get 160.

$$8x-4+160=40$$

Add -4 and 160 to get 156.

$$8x+156=40$$

Subtract 156 from both sides.

$$8x=40-156$$

Subtract 156 from 40 to get -116.

$$8x=-116$$

Divide both sides by 8.

$$x=\frac{-116}{8}$$

Reduce the fraction \frac{-116}{8} to lowest terms by extracting and canceling out 4.

$$x=-\frac{29}{2}$$

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

$$\frac{3\left(-\frac{29}{2}\right)+1}{2}-\frac{3y+2}{4}=0$$

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\left(3\left(-\frac{29}{2}\right)+1\right)-\left(3y+2\right)=0$$

Multiply 3 and -\frac{29}{2} to get -\frac{87}{2}.

$$2\left(-\frac{87}{2}+1\right)-\left(3y+2\right)=0$$

Add -\frac{87}{2} and 1 to get -\frac{85}{2}.

$$2\left(-\frac{85}{2}\right)-\left(3y+2\right)=0$$

Multiply 2 and -\frac{85}{2} to get -85.

$$-85-\left(3y+2\right)=0$$

To find the opposite of 3y+2, find the opposite of each term.

$$-85-3y-2=0$$

Subtract 2 from -85 to get -87.

$$-87-3y=0$$

Add 87 to both sides. Anything plus zero gives itself.

$$-3y=87$$

Divide both sides by -3.

$$y=\frac{87}{-3}$$

Divide 87 by -3 to get -29.

$$y=-29$$

The system is now solved.

$$x=-\frac{29}{2} y=-29$$