Solve {l}{(D_{1}):y=1/2x+3et(D_{1}):y=3-2x}{text{Alorslesdroites}(D_{1})e^prime(D_{2})}

$$\left. \begin{array} { l } { ( D _ { 1 } ) : y = \frac { 1 } { 2 } x + 3 e t ( D _ { 1 } ) : y = 3 - 2 x } \\ { \text { Alors les droites } ( D _ { 1 } ) e ^ { \prime } ( D _ { 2 } ) } \end{array} \right.$$

Solve for x

$$x=-\frac{2D_{1}\left(3et-1\right)}{y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2y, the least common multiple of y,2.

$$2D_{1}=\frac{1}{2}x\times 2y+2\times 3etD_{1}$$

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

$$2D_{1}=xy+2\times 3etD_{1}$$

Multiply 2 and 3 to get 6.

$$2D_{1}=xy+6etD_{1}$$

Swap sides so that all variable terms are on the left hand side.

$$xy+6etD_{1}=2D_{1}$$

Subtract 6etD_{1} from both sides.

$$xy=2D_{1}-6etD_{1}$$

The equation is in standard form.

$$yx=2D_{1}-6eD_{1}t$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{2D_{1}-6eD_{1}t}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{2D_{1}-6eD_{1}t}{y}$$

Divide 2D_{1}-6D_{1}et by y.

$$x=\frac{2D_{1}\left(1-3et\right)}{y}$$