Solve {l}{2x-1y=2}{x-2/5=x-7/4}

$$\left. \begin{array} { l } { 2 x - 1 y = 2 } \\ { \frac { x - 2 } { 5 } = \frac { x - 7 } { 4 } } \end{array} \right.$$

Solve for x, y

$$x=27$$

$$y=52$$

Solution Steps

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

$$4\left(x-2\right)=5\left(x-7\right)$$

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

$$4x-8=5\left(x-7\right)$$

Use the distributive property to multiply 5 by x-7.

$$4x-8=5x-35$$

Subtract 5x from both sides.

$$4x-8-5x=-35$$

Combine 4x and -5x to get -x.

$$-x-8=-35$$

Add 8 to both sides.

$$-x=-35+8$$

Add -35 and 8 to get -27.

$$-x=-27$$

Divide both sides by -1.

$$x=\frac{-27}{-1}$$

Fraction \frac{-27}{-1} can be simplified to 27 by removing the negative sign from both the numerator and the denominator.

$$x=27$$

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

$$2\times 27-y=2$$

Multiply 2 and 27 to get 54.

$$54-y=2$$

Subtract 54 from both sides.

$$-y=2-54$$

Subtract 54 from 2 to get -52.

$$-y=-52$$

Divide both sides by -1.

$$y=\frac{-52}{-1}$$

Fraction \frac{-52}{-1} can be simplified to 52 by removing the negative sign from both the numerator and the denominator.

$$y=52$$

The system is now solved.

$$x=27 y=52$$