SOLUTION: hi please could you help me with the following question: Draw a suitable graph to find the estimates of the solutions of the simultaneous equations. {{{ x^2 + y^2 = 49 and x+y

Algebra ->  Linear-equations -> SOLUTION: hi please could you help me with the following question: Draw a suitable graph to find the estimates of the solutions of the simultaneous equations. {{{ x^2 + y^2 = 49 and x+y      Log On


   

Question 1006945: hi please could you help me with the following question:
Draw a suitable graph to find the estimates of the solutions of the simultaneous equations.
+x%5E2+%2B+y%5E2+=+49+and++x%2By=5+
I have tried to find out the plots to fill in the graph and have got some results for the x+y=5 line.
for this I got
x= 1 y = 4, x=2 7=3, x=3 y=2 and x=4 y=1
but I am unsure if these are correct and also am confused when doing the other line to find out the final answer.
Thank you in advance.
Found 3 solutions by Alan3354, MathLover1, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Draw a suitable graph to find the estimates of the solutions of the simultaneous equations.
+x%5E2+%2B+y%5E2+=+49+and++x%2By=5+
I have tried to find out the plots to fill in the graph and have got some results for the x+y=5 line.
for this I got
x= 1 y = 4, x=2 7=3, x=3 y=2 and x=4 y=1
but I am unsure if these are correct and also am confused when doing the other line to find out the final answer.
--------------------
All your values are points on the line x+y = 5
----
You have to graph the circle and the line, and see where the 2 intersect.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E2+%2B+y%5E2+=+49 ..........eq.1
x%2By=5+.........eq.2
---------------------------
x%2By=5+.........eq.2.........solve for x
x=5-y+.....substitute in eq.1

+%285-y%29%5E2+%2B+y%5E2+=+49 ..........eq.1 ..solve for y
+25-10y%2By%5E2+%2B+y%5E2+=+49
+2y%5E2-10y+=+49-25
+2y%5E2-10y+=+24......both sides divide by 2
+y%5E2-5y+=+12
+y%5E2-5y+-12=0...use quadratic formula

y+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A%28-12%29+%29%29%2F%282%2A1%29+

y+=+%285+%2B-+sqrt%28+25%2B48+%29%29%2F2+
y+=+%285+%2B-+sqrt%28+73+%29%29%2F2+
exact solutions:
y+=+5%2F2+%2B+sqrt%28+73+%29%2F2+
or
y+=+5%2F2+-+sqrt%28+73+%29%2F2+
now find x
x=5-y+
x=5-%285%2F2+%2B+sqrt%28+73+%29%2F2%29+
x=10-5%2F2-sqrt%28+73+%29%2F2%29+
x=5%2F2-sqrt%28+73+%29%2F2%29+
or

x=5-%285%2F2+-+sqrt%28+73+%29%2F2%29+
x=10%2F2-5%2F2%2Bsqrt%28+73+%29%2F2%29+
x=5%2F2%2Bsqrt%28+73+%29%2F2%29+

so, exact solutions:
x=5%2F2-sqrt%28+73+%29%2F2%29+, y+=+5%2F2+%2B+sqrt%28+73+%29%2F2+
or
x=5%2F2%2Bsqrt%28+73+%29%2F2%29+, y+=+5%2F2+-+sqrt%28+73+%29%2F2+

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
She found the answers exactly, but you just wanted to estimate them.

x²+y²=49 is a circle with center at the origin and radius 7
x+y=5 is a line intersecting both axes at 5.






From the looks of the graph, the points of intersection look
to be about %28matrix%281%2C3%2C-1%263%2F4%2C%22%2C%22%2C6%263%2F4%29%29 and %28matrix%281%2C3%2C6%263%2F4%2C%22%2C%22%2C-1%263%2F4%29%29  


Edwin