Solve {l}{g{(x)}=0}{h=5*x}{text{Solvefor}itext{where}}{i=h}

$$\left. \begin{array} { l } { g {(x)} = 0 }\\ { h = 5 \cdot x }\\ { \text{Solve for } i \text{ where} } \\ { i = h } \end{array} \right.$$

Solve for g, x, h

$$x=\frac{1}{5}i=0.2i$$

$$g=0$$

$$h=i$$

Solution Steps

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

$$h=i$$

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

$$i=5x$$

Divide both sides by 5.

$$\frac{i}{5}=x$$

Divide i by 5 to get \frac{1}{5}i.

$$\frac{1}{5}i=x$$

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

$$x=\frac{1}{5}i$$

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

$$g\times \left(\frac{1}{5}i\right)=0$$

Divide both sides by \frac{1}{5}i. Zero divided by any non-zero number gives zero.

$$g=0$$

The system is now solved.

$$g=0 x=\frac{1}{5}i h=i$$