Solve the simultaneous equations for x and y:?

Question

y= x^2 + 7x - 11
y= x - 1

Plz help I will give best answer if I can understand!!! thanks...

Answer 1

The left sides of the two equations are y. This means that the right sides have to be equal:

x^2 + 7x - 11 = x - 1

Now the equation has only one varialbe, so it can be solved for x. One side of the equation needs to be made equal to zero so that we can either factor or use the quadratic formula. Subtract x from both sides and add 1 to both sides to accomplish this:

x^2 + 6x - 10 = 0

There is no easy factoring of this equation, so you need to use the quadratic formula:

x = [-b + sqrt(b^2 - 4ac)]/2a or x = [-b - sqrt(b^2 - 4ac)]/2a

Substituting a = 1, b = 6, and c = -10:

x= [-6 + sqrt(6^2 - 4(1)(-10)]/(2)(1) or
x = [-6 - sqrt(6^2 - 4(1)(-10)]/(2)(1)

x = [-6 + sqrt(76)]/2 or
x = [-6 - sqrt(76)]/2

76 can be factored into 4*19, which means that sqrt(116) = sqrt(4*19) = sqrt(4)*sqrt(19) = 2*sqrt(19) Substituting this you get:

x = [-6 + 2*sqrt(19)]/2 or
x = [-6 - 2*sqrt(19)]/2

Now you can distribute the division by 2 through each term so that you can get the simplest answer:

x = -3 + sqrt(19) or
x = -3 - sqrt(19)

Now that you have x, you can substitute back into the original equation to find out what y is for each solution to x. The bottom equation is the easiest to use, so subtract 1 from x. When you do this, you get these final solutions:

x = -3 + sqrt(19) and y = -4 + sqrt(19) or
x = -3 - sqrt(19) and y = -4 - sqrt(19)

Answer 2

once you think of you have made a mistake, possibilities are high which you have. Redo each little thing from the beginning up, and you will probably discover it. x² + (3x + a million)² = 5 x² + 9x² + 6x + a million = 5 10x² + 6x - 4 = 0 5x² + 3x - 2 = 0 (5x - 2)(x + a million) = 0 x = (2/5) or -a million replace each and each of thes values into the linear equation; verify them in the different one. y = 3(2/5) + a million = 11/5 y = 3(-a million) + a million = -2 (2/5, 11/5) (-a million, -2)

Answer 3

Substitute x = y+1 and get
y = (y+1)²+7(y+1) - 11
y = y²+2y+2+7y+7-11
y = y²+9y-2
0=y²+8y-2
Solve this with the quadratic formula for the two y values (call them y1 and y2). Then the corresponding x values will be
x1=y1+1
x2=y2+2
and you're all done.

HTH

Doug

Answer 4

x (squared) + 7x - 11 = x -1

x(squared) + 6x - 10 =0

x = {-6 (+ or -) squareroot(96) } / 2

x = -3 (+ or -) 2(squareroot(6))

x = 2*(squareroot (6)) - 3
or
x=-2*(squareroot(6)) - 3