Question

2a. $4x - 2y = 8$
work:
$4(0) - 2y = 8$
$ - 2y = 8$
$y = -4$
$4x - 2(0) = 8$
$4x = 8$
$x = 2$
graph 1a & 1b below
solution:
2b. $y + 3x = 1$
work
$1y + 3(0) = 1$
$1y = 1$
$y = 1$
$1(0) + 3x = 1$
$3x = 1$
$x = \frac{1}{3}$
graph 2a & 2b to the right
solution:

Explanation:

Step1: Analyze Equation 2a ($4x - 2y = 8$)

To find the y - intercept, set $x = 0$:
$4(0)-2y = 8\implies - 2y=8\implies y=-4$. So the point is $(0, - 4)$.
To find the x - intercept, set $y = 0$:
$4x-2(0)=8\implies4x = 8\implies x = 2$. So the point is $(2,0)$.

Step2: Analyze Equation 2b ($y + 3x = 1$)

To find the y - intercept, set $x = 0$:
$y+3(0)=1\implies y = 1$. So the point is $(0,1)$.
To find the x - intercept, set $y = 0$:
$0 + 3x=1\implies x=\frac{1}{3}$. So the point is $(\frac{1}{3},0)$.

Step3: Graph the Lines

Plot the points for $4x - 2y = 8$: $(0,-4)$ and $(2,0)$.
Plot the points for $y + 3x = 1$: $(0,1)$ and $(\frac{1}{3},0)$.
Draw the lines through these points.

Step4: Find the Intersection

The intersection of the two lines $4x - 2y = 8$ and $y+3x = 1$ is found by solving the system:
From $y+3x = 1$, we have $y=1 - 3x$.
Substitute into $4x - 2y = 8$:
$4x-2(1 - 3x)=8\implies4x-2 + 6x=8\implies10x=10\implies x = 1$.
Then $y=1-3(1)=-2$. So the solution is $(1,-2)$.

Answer:

The solution of the system of equations (from Graph 2a & 2b) is $(1, - 2)$