Solve {l}{3(4-y)+2=y-6}{2(x-y)+5x-4=0}

$$\left\{ \begin{array} { l } { 3 ( 4 - y ) + 2 = y - 6 } \\ { 2 ( x - y ) + 5 x - 4 = 0 } \end{array} \right.$$

Solve for y, x

$$x=2$$

$$y=5$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 3 by 4-y.

$$12-3y+2=y-6$$

Add 12 and 2 to get 14.

$$14-3y=y-6$$

Subtract y from both sides.

$$14-3y-y=-6$$

Combine -3y and -y to get -4y.

$$14-4y=-6$$

Subtract 14 from both sides.

$$-4y=-6-14$$

Subtract 14 from -6 to get -20.

$$-4y=-20$$

Divide both sides by -4.

$$y=\frac{-20}{-4}$$

Divide -20 by -4 to get 5.

$$y=5$$

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

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

Use the distributive property to multiply 2 by x-5.

$$2x-10+5x-4=0$$

Combine 2x and 5x to get 7x.

$$7x-10-4=0$$

Subtract 4 from -10 to get -14.

$$7x-14=0$$

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

$$7x=14$$

Divide both sides by 7.

$$x=\frac{14}{7}$$

Divide 14 by 7 to get 2.

$$x=2$$

The system is now solved.

$$y=5 x=2$$