SOLUTION: I need your help on this. Please help me understand this better. 1 Instructions: Graph each pair of equations in the same coordinate plane. Find the coordinates of the point wher

Algebra ->  College  -> Linear Algebra -> SOLUTION: I need your help on this. Please help me understand this better. 1 Instructions: Graph each pair of equations in the same coordinate plane. Find the coordinates of the point wher      Log On


   

Question 50521This question is from textbook Algebra and Trigonometry
: I need your help on this. Please help me understand this better.
1
Instructions: Graph each pair of equations in the same coordinate plane. Find the coordinates of the point where the graphs intersect. Then show by substitution that the coordinates satisfy both equations.
3x+2y=0
x-2y=8 This question is from textbook Algebra and Trigonometry

Answer by tutorcecilia(2152) About Me  (Show Source):
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Graph each pair of equations in the same coordinate plane.
3x+2y=0 [Rewrite in y=mx+b formate by solving for y]
3x-3x+2y=-3x [Solve for y]
2y=-3x
2y/2=-3/2x
y=-3/2x + 0 Graph with a slope of (-3/2) and a y-intercept of (0, 0)
.
.
x-2y=8 [Rewrite in y=mx+b formate by solving for y]
x-x-2y=-x+8
-2y=-x+8
-2y/-2=-x/-2+8/-2
y=1/2x-4 [Graph with a slope of (1/2) and a y-intercept of (0, -4)
.
Graphing:
+graph%28+300%2C+200%2C+-6%2C+5%2C+-6%2C+10%2C+%28-3%2F2%29x%2B0%2C+%281%2F2%29x-4%29+

.
Find the coordinates of the point where the graphs intersect.
Looking at the graph, the two lines intersect or cross at points (2, -3).
Plug (2, -4) into each original equation to prove that these are the common points.
.

Then show by substitution that the coordinates satisfy both equations.
3x+2y=0 [Plug-in points (2, -3)
3(2)+2(-3)=0 [Solve]
6-6=0
0=0 [Proved that (2, -3) are points of this line]
.
x-2y=8 [Plug-in points (2, -3)
(2)-2(-3)=8
2+6=8
8=8 {Proved that (2, -3 ) are points of this line also]