SOLUTION: 2x-3y =18 and 5x +3y =3 solutions ( 3 ,4) dont understand how my book got the solution 3 need a full break down

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Question 187386: 2x-3y =18 and 5x +3y =3

solutions ( 3 ,4) dont understand how my book got the solution 3 need a full break down
Found 2 solutions by jojo14344, Earlsdon:
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Givensystem%282x-3y+=18+%28EQN1%29%2C5x+%2B3y+=3%28EQN2%29%29
In EQN 1 we get:
3y=2x-18---->cross%283%29y%2Fcross%283%29=%282x-18%29%2F3
y=%282%2F3%29x-%2818%2F3%29=%282%2F3%29x-6 EQN 3, subst. in EQN 2:
5x%2B3%28highlight%28%282%2F3%29x-6%29%29=3
5x%2B%286%2F3%29x-18=3---->5x%2B2x-18=3---->7x=3%2B18=21--->cross%287%29x%2Fcross%287%29=21%2F7=3
red%28x=3%29, Subst. in EQN 3:
y=%282%2Fcross%283%29%29%28cross%283%29%29-6=2-6=-4
red%28y=-4%29
Therefore, point of Intersection (3,-4)
We see graph:
--> RED Line (EQN 1); GREEN Line (EQN 2)
Thank you,
Jojo


Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:
2x-3y+=+18
5x%2B3y+=+3 Add these two equations:
--------------
7x+=+21 Divide both sides by 7.
x+=+3 Now substitute this value of x into either one of the two given equations and solve for y.
5x%2B3y+=+3 Substitute x = 3.
5%283%29%2B3y+=+3 Simplify.
15%2B3y+=+3 Subtract 15 from both sides.
3y+=+-12 Finally, divide both sides by 3.
y+=+-4
The solution is (3, -4)
See the graph, the solution is the point of intersection of the two lines:
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C%282%2F3%29x-6%2C%28-5%2F3%29x%2B1%29