Trying to figure out how they are coming up with 2,3 and not 5,3
Thanks
4x+3y=17
2x+3y=13
subtract the 2nd equation from the 1st
you'll get 2x = 4
after solving you'll get x= 2
and put the value of x in any of the above eqn you'll get y
4x+3y=17
2x+3y=13
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4x+3y=17
(2x+3y=13) - multi ply by -2 to the x terms. Now add . . . .
4x + 3y = 17
-4x - 6y = -26
0 - 3y = -9
y =-9/-3 = 3
Next,
4x+3y=17
2x+3y=13, multiply by -1 to eliminate y terms,
4x +3y = 17
-2x - 3y = -13 then add,
?
Just a note: It should make no difference whether they add or substract the equations -- either way there is one unique solution.
If you choose to add them, you get:
$\displaystyle 4x+3y+2x+3y=17+13 \Rightarrow 6x+6y = 30 \Rightarrow 6(x+y) = 6*5$ $\displaystyle \Rightarrow x+y = 5 \Rightarrow x = 5-y$
Now substitute that into either equation, let's say the first:
$\displaystyle 4(5-y)+3y = 17 \Rightarrow 20-4y+3y=17\Rightarrow -y = -3 \Rightarrow y = 3 \Rightarrow x + 3 = 5$ $\displaystyle \Rightarrow \boxed{x=2, y=3}$