Solve {l}{3x+11/4-y+1/3=23/6}{2x-1/2-frac{4+3}{4}=frac{1}{4}}

$$\left\{ \begin{array} { l } { \frac { 3 x + 11 } { 4 } - \frac { y + 1 } { 3 } = \frac { 23 } { 6 } } \\ { \frac { 2 x - 1 } { 2 } - \frac { 4 + 3 } { 4 } = \frac { 1 } { 4 } } \end{array} \right.$$

Solve for x, y

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

$$y = \frac{11}{8} = 1\frac{3}{8} = 1.375$$

Solution Steps

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

$$2\left(2x-1\right)-\left(4+3\right)=1$$

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

$$4x-2-\left(4+3\right)=1$$

Add 4 and 3 to get 7.

$$4x-2-7=1$$

Subtract 7 from -2 to get -9.

$$4x-9=1$$

Add 9 to both sides.

$$4x=1+9$$

Add 1 and 9 to get 10.

$$4x=10$$

Divide both sides by 4.

$$x=\frac{10}{4}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$x=\frac{5}{2}$$

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

$$\frac{3\times \frac{5}{2}+11}{4}-\frac{y+1}{3}=\frac{23}{6}$$

Multiply both sides of the equation by 12, the least common multiple of 4,3,6.

$$3\left(3\times \frac{5}{2}+11\right)-4\left(y+1\right)=46$$

Multiply 3 and \frac{5}{2} to get \frac{15}{2}.

$$3\left(\frac{15}{2}+11\right)-4\left(y+1\right)=46$$

Add \frac{15}{2} and 11 to get \frac{37}{2}.

$$3\times \frac{37}{2}-4\left(y+1\right)=46$$

Multiply 3 and \frac{37}{2} to get \frac{111}{2}.

$$\frac{111}{2}-4\left(y+1\right)=46$$

Use the distributive property to multiply -4 by y+1.

$$\frac{111}{2}-4y-4=46$$

Subtract 4 from \frac{111}{2} to get \frac{103}{2}.

$$\frac{103}{2}-4y=46$$

Subtract \frac{103}{2} from both sides.

$$-4y=46-\frac{103}{2}$$

Subtract \frac{103}{2} from 46 to get -\frac{11}{2}.

$$-4y=-\frac{11}{2}$$

Divide both sides by -4.

$$y=\frac{-\frac{11}{2}}{-4}$$

Express \frac{-\frac{11}{2}}{-4} as a single fraction.

$$y=\frac{-11}{2\left(-4\right)}$$

Multiply 2 and -4 to get -8.

$$y=\frac{-11}{-8}$$

Fraction \frac{-11}{-8} can be simplified to \frac{11}{8} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{11}{8}$$

The system is now solved.

$$x=\frac{5}{2} y=\frac{11}{8}$$