Answer
$i_{1}=1$mA
$i_{2}=3$mA
Work Step by Step
To solve this system of equations, we use the graphing method.
$3i_{1}+4i_{2}=15$
$5i_{1}-2i_{2}=-1$
Taking the first equation, we solve for $i_{2}$.
$3i_{1}+4i_{2}=15$
$4i_{2}=15-3i_{1}$
$i_{2}=\frac{15-3i_{1}}{4}$
Find three solutions:
For $i_{1}=2$,
$i_{2}=\frac{15-3i_{1}}{4}$
$i_{2}=\frac{15-3(2)}{4}$
$i_{2}=\frac{15-6}{4}$
$i_{2}=\frac{9}{4}=2.25$
For $i_{1}=0$,
$i_{2}=\frac{15-3i_{1}}{4}$
$i_{2}=\frac{15-3(0)}{4}$
$i_{2}=\frac{15-0}{4}$
$i_{2}=\frac{15}{4}=3.75$
For $i_{1}=-2$,
$i_{2}=\frac{15-3i_{1}}{4}$
$i_{2}=\frac{15-3(-2)}{4}$
$i_{2}=\frac{15+6}{4}$
$i_{2}=\frac{21}{4}=5.25$
With the three points, $(2,2.25), (0,3.75), (-2,5.25)$, we can graph the straight line that goes through these points.
Taking the second equation, we solve for $i_{2}$.
$5i_{1}-2i_{2}=-1$
$-2i_{2}=-1-5i_{1}$
$i_{2}=\frac{5i_{1}+1}{2}$
Find three solutions:
For $i_{1}=2$,
$i_{2}=\frac{5i_{1}+1}{2}$
$i_{2}=\frac{5(2)+1}{2}$
$i_{2}=\frac{10+1}{2}$
$i_{2}=\frac{11}{2}=5.5$
For $i_{1}=0$,
$i_{2}=\frac{5i_{1}+1}{2}$
$i_{2}=\frac{5(0)+1}{2}$
$i_{2}=\frac{0+1}{2}$
$i_{2}=\frac{1}{2}=0.5$
For $i_{1}=-2$,
$i_{2}=\frac{5i_{1}+1}{2}$
$i_{2}=\frac{5(-2)+1}{2}$
$i_{2}=\frac{-10+1}{2}$
$i_{2}=\frac{-9}{2}=-4.5$
With the three points, $(2,5.5), (0,0.5), (-2,-4.5)$, we can graph the straight line that goes through these points.
The intersection point between these two lines is the answer to the system of equations.
