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

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

Solve for x, y

$$x = \frac{21}{4} = 5\frac{1}{4} = 5.25$$

$$y=7$$

Solution Steps

Consider the second equation. Multiply both sides of the equation by 10, the least common multiple of 2,5.

$$5\left(2-4\right)+2\left(y-2\right)=0$$

Subtract 4 from 2 to get -2.

$$5\left(-2\right)+2\left(y-2\right)=0$$

Multiply 5 and -2 to get -10.

$$-10+2\left(y-2\right)=0$$

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

$$-10+2y-4=0$$

Subtract 4 from -10 to get -14.

$$-14+2y=0$$

Add 14 to both sides. Anything plus zero gives itself.

$$2y=14$$

Divide both sides by 2.

$$y=\frac{14}{2}$$

Divide 14 by 2 to get 7.

$$y=7$$

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

$$\frac{x-3}{3}-\frac{7-4}{4}=0$$

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

$$4\left(x-3\right)-3\left(7-4\right)=0$$

Use the distributive property to multiply 4 by x-3.

$$4x-12-3\left(7-4\right)=0$$

Subtract 4 from 7 to get 3.

$$4x-12-3\times 3=0$$

Multiply -3 and 3 to get -9.

$$4x-12-9=0$$

Subtract 9 from -12 to get -21.

$$4x-21=0$$

Add 21 to both sides. Anything plus zero gives itself.

$$4x=21$$

Divide both sides by 4.

$$x=\frac{21}{4}$$

The system is now solved.

$$x=\frac{21}{4} y=7$$