Solve {c}{-3x+11y-1=-7x+2y+7}{x/5-4/4=2/5}

$$\left\{ \begin{array} { c } { - 3 x + 11 y - 1 = - 7 x + 2 y + 7 } \\ { \frac { x } { 5 } - \frac { 4 } { 4 } = \frac { 2 } { 5 } } \end{array} \right.$$

Solve for x, y

$$x=7$$

$$y = -\frac{20}{9} = -2\frac{2}{9} \approx -2.222222222$$

Solution Steps

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

$$4x-5\times 4=8$$

Multiply -5 and 4 to get -20.

$$4x-20=8$$

Add 20 to both sides.

$$4x=8+20$$

Add 8 and 20 to get 28.

$$4x=28$$

Divide both sides by 4.

$$x=\frac{28}{4}$$

Divide 28 by 4 to get 7.

$$x=7$$

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

$$-3\times 7+11y-1=-7\times 7+2y+7$$

Multiply -3 and 7 to get -21.

$$-21+11y-1=-7\times 7+2y+7$$

Subtract 1 from -21 to get -22.

$$-22+11y=-7\times 7+2y+7$$

Multiply -7 and 7 to get -49.

$$-22+11y=-49+2y+7$$

Add -49 and 7 to get -42.

$$-22+11y=-42+2y$$

Subtract 2y from both sides.

$$-22+11y-2y=-42$$

Combine 11y and -2y to get 9y.

$$-22+9y=-42$$

Add 22 to both sides.

$$9y=-42+22$$

Add -42 and 22 to get -20.

$$9y=-20$$

Divide both sides by 9.

$$y=-\frac{20}{9}$$

The system is now solved.

$$x=7 y=-\frac{20}{9}$$