Question

PLEASEEE HELP MEEEE!!!

solve these pairs of simultaneous equations:

c)
${x}^{2} + {y}^{2} = 13$
$5y + x = 13$

Answer 1

Use substitution

From second equation:-

x = 13 - 5y,                   Substitute for x in the first eqaution:

(13 - 5y)^2 + y^2 = 13

169 -130y + 25y^2 + y^2 - 13 = 0

26y^2  - 130y + 156  = 0

26(y^2 - 5y + 6) = 0

26(y - 3)(y - 2) = 0

y = 2 , y = 3

From the second equation when y = 2, x =  13 - 5(2) = 3

and when y = 3,  x = 13 - 5(3) = -2

So the solution is   [3, 2} and {-2, 3}