Simultaneous Equation??

Question

can you solve:
y=7x-9
y=x^2 + 1

thank you

p.s. can you show how it was done?

Answer 1

x^2 + 1 = 7x - 9
x^2 - 7x + 10 = 0
(x - 5) ( x - 2) = 0
x = 5, x = 2

Answer 2

1) y = 7x - 9
2) y = x^2 + 1

Since both of the equations are solved for y, set them equal to each other

x^2 + 1 = 7x - 9
x^2 - 7x + 10 = 0
(x - 5)(x - 2) = 0

x = 5, x = 2

1) y = 7(5) - 9 = 35 - 9 = 26
2) y = 5^2 + 1 = 25 + 1 = 26

When x = 5, y = 26

1) y = 7(2) - 9 = 14 - 9 = 5
2) y = 2^2 + 1 = 4 + 1 = 5

When x = 2, y = 5

Answer 3

One way to solve simultaneous equations is to insert one equation into the other.

So we know that y=7x-9 and y=x^2+1 so we can replace y with 7x-9.

7x-9=x^2+1

You then need to rearrange the formula so you can solve it. With this one you need to turn it into a quadratic equation because you have an x^2. So move all the values to one side to leave the other side as 0.

x^2+1+9-7x=0
X^2-7x+10=0

Then you have to factorize the equation.

(x-5)(x-2)=0

Now, because you know that it equals zero we know that either (x-5)=0 or (x-2)=0 (because the only way to get 0 as the result of a multiplication is for one of the values to be zero). So we are going to get two results.

if x-5=0 then x=5

if x-2=0 then x=2

So the two results for x are 5 and 2. But remember we still need to work out y. To do that all we need to do is substitute our values into the equation, first 5, then 2.

y=7x-9

If x=5

y=7*5-9
y=26

If x=2

y=7*2-9
y=5

So, all the values for y and x are:

x=5 and y=26

or

x=2 and y=5

Answer 4

y = 7x - 9

y = x^2 +1

Take first equation substitue for y in second equation:

7x - 9 = x^2+1 now do some algebra

0 = x^2 - 7x +10

0 = (x - 5)(x - 2)

x = +2, +5

Answer 5

It cant be solved by simultaneous equations, however, if you put them equal to each other...

x^2 + 1 = 7x - 9

You can bring them over and get a quadratic...

x^2 - 7x + 10

(x-5)(x-2)

Hence

x = 5 and x =2

Answer 6

x² + 1 = 7x - 9
x² - 7x + 10 = 0
(x - 5) (x - 2) = 0
x = 2 , x = 5

Answer 7

y= 7x-9 y=7x
-9y=9(x^2)-9 -9y=9(x^2) wait... impossible. not evough numeric values to get an accurae answer

Answer 8

y=7x-9
y=x^2+1 (subract them)
-------------
0=7x-x^2-10

change signs

x^2-7x+10=0
x^2-5x-2x+10=0
x(x-5)-2(x-5)=0
(x-5)(x-2)=0
x=5, x=2

if x=5, then for y
y= 7x-9
y=7(5)-9
y=35-9
y=26


if x=2, then for y
y= 7x-9
y=7(2)-9
y=14-9
y=5