Solve {l}{x/2-y+2/2=3/6}{2(x-1)/3-frac{7+2}{6}=-1}

$$\left\{ \begin{array} { l } { \frac { x } { 2 } - \frac { y + 2 } { 2 } = \frac { 3 } { 6 } } \\ { \frac { 2 ( x - 1 ) } { 3 } - \frac { 7 + 2 } { 6 } = - 1 } \end{array} \right.$$

Solve for x, y

$$x = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

$$y = -\frac{5}{4} = -1\frac{1}{4} = -1.25$$

Solution Steps

Consider the second equation. Multiply both sides of the equation by 6, the least common multiple of 3,6.

$$2\times 2\left(x-1\right)-\left(7+2\right)=-6$$

Multiply 2 and 2 to get 4.

$$4\left(x-1\right)-\left(7+2\right)=-6$$

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

$$4x-4-\left(7+2\right)=-6$$

Add 7 and 2 to get 9.

$$4x-4-9=-6$$

Subtract 9 from -4 to get -13.

$$4x-13=-6$$

Add 13 to both sides.

$$4x=-6+13$$

Add -6 and 13 to get 7.

$$4x=7$$

Divide both sides by 4.

$$x=\frac{7}{4}$$

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

$$\frac{\frac{7}{4}}{2}-\frac{y+2}{2}=\frac{3}{6}$$

Multiply both sides of the equation by 6, the least common multiple of 2,6.

$$3\times \frac{7}{4}-3\left(y+2\right)=3$$

Multiply 3 and \frac{7}{4} to get \frac{21}{4}.

$$\frac{21}{4}-3\left(y+2\right)=3$$

Use the distributive property to multiply -3 by y+2.

$$\frac{21}{4}-3y-6=3$$

Subtract 6 from \frac{21}{4} to get -\frac{3}{4}.

$$-\frac{3}{4}-3y=3$$

Add \frac{3}{4} to both sides.

$$-3y=3+\frac{3}{4}$$

Add 3 and \frac{3}{4} to get \frac{15}{4}.

$$-3y=\frac{15}{4}$$

Divide both sides by -3.

$$y=\frac{\frac{15}{4}}{-3}$$

Express \frac{\frac{15}{4}}{-3} as a single fraction.

$$y=\frac{15}{4\left(-3\right)}$$

Multiply 4 and -3 to get -12.

$$y=\frac{15}{-12}$$

Reduce the fraction \frac{15}{-12} to lowest terms by extracting and canceling out 3.

$$y=-\frac{5}{4}$$

The system is now solved.

$$x=\frac{7}{4} y=-\frac{5}{4}$$