Two numbers that add to give 7 and multiply to give -60?

Question

x+y=7
x*y=-60

Answer 1

Try +12 and -5

Answer 2

Another approach is to consider the factors of 60

1, 60, 2, 30, 3, 20, 4, 15, 5, 12, 6, 10

Only the 5, 12 pair can be used to add to 7

-5 and 12

Answer 3

x+y=7 gives x=(7-y)
Substitute this in the second equation. We get
(7-y)*(y)=-60, i.e.,
7y - y^2 =-60, or
y^2 -7y - 60=0
y^2 -12y +5y - 60=0
y(y-12) +5(y-12) =0
Thus (y-12)*(y+5)=0
This gives two solutions
y = 12
and
y = - 5
With y=12, we get x= - 5, and with y= -5, we get x = 12
Thus there are two solutions
x = -5 , y = 12
and
x = 12, y = -5

Answer 4

x + y = 7
x * y = -60

x + y = 7
y = -x + 7

x(-x + 7) = -60
-x^2 + 7x = -60
x^2 - 7x - 60 = 0
(x - 12)(x + 5) = 0

x = 12 or -5

y = -x + 7
y = -(12 or -5) + 7
y = (-12 or 5) + 7
y = -5 or 12

ANS : 12 and -5

Answer 5

x+y=7
y=-x+7

x*y=-60
x*(-x+7)=-60
-x^2+7x=-60
-x^2+7x+60=0

Quadratic Equation
x=[-b+SQRT(b^2-4ac)]/2a and x=[-b-SQRT(b^2-4ac)]/2a
x=[-7+SQRT(7^2-(4)(-1)(60))]/2*(-1) and x=[-7-SQRT(7^2-(4)(-1)(60))]/2*(-1)
x=[-7+SQRT(49+240)/(-2) and x=[-7-SQRT(49+240)/(-2)
x={-7+SQRT(289)/(-2) and x={-7-SQRT(289)/(-2)
x=(-7+17)/(-2) and x=(-7-17)/(-2)
x=-10/(-2) and x=-24/(-2)
x=-5 and x=12

x+y=7
-5+y=7 or 12+y=7
y=12 or y=-5

Answer 6

-5 and 12

you can do the rest of your homework yourself!