Solve graphically. An electric circuit containing two currents may be expressed by the equation $\begin{array} { l } 3 i _ { 1 } + 4 i _ { 2 } = 41 \ 5 i _ { 1 } - 2 i _ { 2 } = 25 \end{array}$ where i ₁ and i ₂ are the currents in microamperes ( $\mu A$ ). Find the two currents.

Question

Quizplus · Accepted Answer

To solve the system graphically, we can rewrite each equation in slope-intercept form:
$$
i_{1}=-\frac{3}{4}i_{2}+\frac{41}{4}
$$
$$
i_{2}=\frac{5}{2}i_{1}-\frac{25}{2}
$$
We can then plot these lines on a coordinate plane and see where they intersect:

![graph](https://i.imgur.com/bLaJp3G.png)

The intersection point is approximately (6, 13), so the two currents are:
$$
i_{1}=6\mu A
$$
$$
i_{2}=13\mu A
$$

Solve Graphically 3i1+4i2=415i1−2i2=25\begin{array} { l } 3 i _ { 1 } + 4 i _ { 2 } = 41 \\5 i _ { 1 } - 2 i _ { 2 } = 25\end{array}3i1​+4i2​=415i1​−2i2​=25​

Solve Graphically $\begin{array} { l } 3 i _ { 1 } + 4 i _ { 2 } = 41 \\5 i _ { 1 } - 2 i _ { 2 } = 25\end{array}$