Solve (alpha+beta)(-8)-1/2*4+8+(4alpha+3beta)=0

$$( \alpha + \beta ) ( - 8 ) - \frac { 1 } { 2 } \cdot 4 + 8 + ( 4 \alpha + 3 \beta ) = 0$$

Solve for α

$$\alpha =-\frac{5\beta }{4}+\frac{3}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \alpha +\beta by -8.

$$-8\alpha -8\beta -\frac{1}{2}\times 4+8+4\alpha +3\beta =0$$

Multiply \frac{1}{2} and 4 to get 2.

$$-8\alpha -8\beta -2+8+4\alpha +3\beta =0$$

Add -2 and 8 to get 6.

$$-8\alpha -8\beta +6+4\alpha +3\beta =0$$

Combine -8\alpha and 4\alpha to get -4\alpha .

$$-4\alpha -8\beta +6+3\beta =0$$

Combine -8\beta and 3\beta to get -5\beta .

$$-4\alpha -5\beta +6=0$$

Add 5\beta to both sides. Anything plus zero gives itself.

$$-4\alpha +6=5\beta$$

Subtract 6 from both sides.

$$-4\alpha =5\beta -6$$

Divide both sides by -4.

$$\frac{-4\alpha }{-4}=\frac{5\beta -6}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$\alpha =\frac{5\beta -6}{-4}$$

Divide 5\beta -6 by -4.

$$\alpha =-\frac{5\beta }{4}+\frac{3}{2}$$

Solve for β

$$\beta =\frac{6-4\alpha }{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \alpha +\beta by -8.

$$-8\alpha -8\beta -\frac{1}{2}\times 4+8+4\alpha +3\beta =0$$

Multiply \frac{1}{2} and 4 to get 2.

$$-8\alpha -8\beta -2+8+4\alpha +3\beta =0$$

Add -2 and 8 to get 6.

$$-8\alpha -8\beta +6+4\alpha +3\beta =0$$

Combine -8\alpha and 4\alpha to get -4\alpha .

$$-4\alpha -8\beta +6+3\beta =0$$

Combine -8\beta and 3\beta to get -5\beta .

$$-4\alpha -5\beta +6=0$$

Add 4\alpha to both sides. Anything plus zero gives itself.

$$-5\beta +6=4\alpha$$

Subtract 6 from both sides.

$$-5\beta =4\alpha -6$$

Divide both sides by -5.

$$\frac{-5\beta }{-5}=\frac{4\alpha -6}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$\beta =\frac{4\alpha -6}{-5}$$

Divide 4\alpha -6 by -5.

$$\beta =\frac{6-4\alpha }{5}$$