Simultaneous Equations HELP.. GCSE/Alevel maths bridging work?

Question

Solve..

7x^2 + y^2 = 64
x + y = 4

I dont get it with there being squared signs in.. I can do simultaneous equations usually...

This work is due in tomorrow by the way!

Thanks...

Answer 1

7x^2 + y^2 = 64
x + y = 4 => y = 4 - x

7x^2 + (4-x)^2 = 64
7x^2 + 16 - 8x + x^2 = 64
8x^2 - 8x -48 = 0
8(x^2 - x - 6) = 0
(x - 3)(x + 2) = 0
x = 3 or -2
y = 1 or 6

Answer 2

y = 4 - x

Stick this in the first guy for y.

7x^2 + 16 - 8x + x^2 = 64
8x^2 - 8x + 16 = 64
x^2 - x + 2 = 8
x^2 - x - 6 = 0
(x - 3)(x + 2) = 0
x is 3 or -1

So y is 1 or 5.

Answer 3

those are common yet while taught incorrect may be problematical. First you look at the two equations: 5x - y = 10 3x + y = 14 So in this equation it particularly is ultimate to resolve for x first. 5x=3x=8x. 5x - y = 10 3x + y = 14 8x plus or minus y so which you y's cancel out. Now the equations reads: 8x=10+14=24 or 8x=24 next divide 24 by utilising 8 and you get x=3 next which you have your x-value. you will be able to desire to replace: (you're you able to the two equation, yet we could use the 1st one) 5(3) - y =10 15-y=10 y=5 you are able to verify this additionally by utilising pluging it interior the the 2d equation: 3x + y =14 3(5)+y=14 15+y=14 y=-a million So.... 5*3-5=10 and 3*3=5=14 So the equation works and has a answer.

Answer 4

solve the simple equation for either x or y

plug it into the second

use the quadratic formula (or factor if you can) to solve

plug the result back into the simple equation to solve for the other variable

x+y=4
x=4-y

7x^2 + y^2 = 64
7(4-y)^2 + y^2 = 64
7 (16-2y+y^2 ) + y^2 = 64
112 - 14y +7y^2 + y^2 = 64
48 - 14y + 8y^2 = 0

(quadratic formula)
y= (approx.) 3.16
x=.84

Answer 5

7x^2 + y^2 = 64 and x + y = 4
square root each side

7x + y = 8 and x + y = 4
-7x -7x -x -x

y = 8 - 7x and y = 4 - x

y=y
8-7x = 4-x
=7x =7x
8 = 4 = 6x
-4 -4
4 = 6x
/6 /6

x = o.67 or 2/3

y = 4 - x
y = 4 - o.67 or 2/3
y = 3.33 or 3 1/3

Answer 6

y=4-x

7x^2+(16-8x+x^2)=64

8x^2-8x+16-64=0

8x^2-8x-48=0

x^2-x-6=0

(x+2)(x-3)=0

x=-2 y=6

x=3 y=1