SOLUTION: 2x+3y=7 3x+4y=10 i need to find teh exact point where these two systems fo equations meet. can anybody help me?

Question 250271: 2x+3y=7
3x+4y=10
i need to find teh exact point where these two systems fo equations meet. can anybody help me?
Found 2 solutions by solver91311, checkley77:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Multiply the first equation by 3. Multiply the second equation by -2. That will leave you with coefficients on the variables that are additive inverses. Add the two equations term by term. The coefficient on in the resulting equation will be zero, thereby eliminating that variable. You will be left with an equation in that can be solved by ordinary means. (In this case, you don't have to do anything. The results of the addition of the two equations leaves you with the value of by inspection.) Take the value of and substitute it back into either of the original equations, then solve for .

The resulting values of and form an ordered pair that is the exact solution of your system. By the way, you do not have two systems. You have two equations that form one system.

John

Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
2x+3y=7
3y=-2x+7
y=-2x/3+7/3 (red line)
------------------
3x+4y=10
4y=-3x+10
y=-3x/4+10/4
y=-3x/4+2.5 (green line)
-------------------------
(graph 300x200 pixels, x from -6 to 5, y from -6 to 5, of TWO functions -2x/3 +7/3 and -3x/4 +2.5 ).
y=-2x/3+7/3
-(y=-3x/4+2.5) subtract
---------------------
0=-2x/3+3x/4+7/3-2.5
0=(-2x*4+3x*3+7*4)/3*4-2.5
0=(-8x+9x+28)/12-2.5
0=(x+28)/12-2.5
(x+28)/12=2.5
x+28=12*2.5
x+28=30
x=30-28
x=2 ans.
y=-2*2/3+7/3
y=-4/3+7/3
y=3/3=1 ans.
Intercept (2,1)

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