No solution
1) Since we are about to solve this system graphically, then let's set two t-tables picking random values for x, plugging them into each function to get at least three coordinate pairs (points), and plot them.
2) Considering the 1st equation:
I) x+2y=3
Let's rewrite into the Slope-intercept form:
[tex]\begin{gathered} x+2y=3 \\ 2y=3-x \\ \frac{2y}{2}=\frac{3}{2}-\frac{x}{2} \\ y=-\frac{x}{2}+\frac{3}{2} \end{gathered}[/tex]x | y
-1 | 2
0 | 3/2
1 | 1
(-1,2) , (0, 3/2), (1,1) These are the points we are going to use, considering that the slope is negative.
II) 3x+6y=15
Rewriting into the Slope intercept form, for convenience, we can set the following t-table.
[tex]\begin{gathered} 3x+6y=15\: \\ 3x+6y=15(\: \div3) \\ x+2y=5 \\ x-x+2y=5-x \\ 2y=5-x \\ \frac{2y}{2}=\frac{5-x}{2} \\ y=\frac{5}{2}-\frac{x}{2} \end{gathered}[/tex]x|y
-1| 3
0| 5/2
1| 2
(-1,3), (0,5/2), (1,2)
3) So let's plot those points considering a decreasing slope for both equations:
his is the graph, as we can see there's no common point to any of those equations (represented by lines). Hence, we can state that There is no solution
