Solve {l}{g{(x)}=-0}{h=4x+0}{text{Solvefor}itext{where}}{i=h}

$$\left. \begin{array} { l } { g {(x)} = -0 }\\ { h = 4 x + 0 }\\ { \text{Solve for } i \text{ where} } \\ { i = h } \end{array} \right.$$

Solve for g, x, h

$$x=\frac{1}{4}i=0.25i$$

$$g=0$$

$$h=i$$

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.

$$i=4x+0$$

Anything plus zero gives itself.

$$i=4x$$

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

$$4x=i$$

Divide both sides by 4.

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

Divide i by 4 to get \frac{1}{4}i.

$$x=\frac{1}{4}i$$

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

$$g\times \left(\frac{1}{4}i\right)=0$$

Divide both sides by \frac{1}{4}i. Zero divided by any non-zero number gives zero.

$$g=0$$

The system is now solved.

$$g=0 x=\frac{1}{4}i h=i$$