# equation

• Aug 24th 2009, 11:45 AM
cliste09
equation
hey i have yet another maths question...:( i tried looking for the solution but the site for the exam papers is down. the question is solve:

for x and y
x + y = 7

x^2+y^2=29

the answer is (2,5) and (5,2) but i got (10,0) and (0,10)

i have ALOT of difficulty with these sums so i would be really grateful for the solution to do it , thanks

then it asks in part (2) " which one of the values of y in the above satisfies the inequality 6-2y<0
• Aug 24th 2009, 11:54 AM
masters
Quote:

Originally Posted by cliste09
hey i have yet another maths question...:( i tried looking for the solution but the site for the exam papers is down. the question is solve:

for x and y
x + y = 7

x^2+y^2=29

the answer is (2,5) and (5,2) but i got (10,0) and (0,10)

i have ALOT of difficulty with these sums so i would be really grateful for the solution to do it , thanks

then it asks in part (2) " which one of the values of y in the above satisfies the inequality 6-2y<0

Hi cliste09,

(1) \$\displaystyle x+y=7\$
(2) \$\displaystyle x^2+y^2=29\$

Solve the (1) equation for x
(1)\$\displaystyle x=7-y\$

Substitute into (2)

\$\displaystyle (7-y)^2+y^2=29\$
\$\displaystyle 49-14y+y^2+y^2-29=0\$
\$\displaystyle 2y^2-14y+20=0\$
\$\displaystyle y^2-7y+10=0\$
\$\displaystyle (y-5)(y-2)=0\$
\$\displaystyle y=5 \ \ or \ \ y=2\$

Substitute each value of y back into (1) to retrieve your x-values. Your points of intersection are (2,5) and (5, 2).

As far as part 2 goes, use your y-values of 5 and 2 and see which one makes the inequality true.
• Aug 24th 2009, 01:02 PM
cliste09
thank you soooo much!!!!! (Happy) your solution is very easy to understand , phew these q's are one of my worst areas in maths ... dont even get me started on trigonometry lol