SOLUTION: solve the simultaneous equations: y=x^2+2x+9 7x+y=19 please show me how u solve it. thank you!

Algebra ->  Systems-of-equations -> SOLUTION: solve the simultaneous equations: y=x^2+2x+9 7x+y=19 please show me how u solve it. thank you!      Log On


   

Question 46819: solve the simultaneous equations:
y=x^2+2x+9
7x+y=19
please show me how u solve it. thank you!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the simultaneous equations (aka: System of equations):
1) y+=+x%5E2%2B2x%2B9
2) 7x%2By+=+19
You can solve this system of equations (aka: Simultaneous equations) by the "susbtitution" method.
Substitute equation 1) into equation 2) for y and solve for x.
7x+%2B+%28x%5E2%2B2x%2B9%29+=+19 Simplify and solve for x.
x%5E2%2B9x%2B9+=+19 Subtract 19 from both sides of the equation.
x%5E2%2B9x-10+=+0 Solve this quadratic equation by factoring.
%28x-1%29%28x%2B10%29+=+0 Apply the zero products principle.
x-1+=+0 and/or x%2B10+=+0
If x-1+=+0 then x+=+1
If x%2B10+=+0 then x+=+-10
Now, to find the value of y, substitute the values of x, one-at-a-time into either of the two original equations and solve for y. Let's take the first equation y+=+x%5E2%2B2x%2B9 and substitute x = 1 then solve for y.
y+=+1%5E2%2B2%281%29%2B9
y+=+12
So one of the solutions is: x = 1, y = 12 or (1,12)
Just as a check, you can see that, had we substituted x = 1 into the second equation, we would have obtained the same result.
7%281%29+%2B+y+=+19 Subtact 7 from both sides.
y+=+12 Same as before.
Now to get the second solution, substitute x = -10 into the first equation and solve for y.
y+=+%28-10%29%5E2%2B2%28-10%29%2B9
y+=+100-20%2B9
y+=+89
Now let's try using the second equation.
7%28-10%29+%2B+y+=+19
-70+%2B+y+=+19 Add 70 to both sides.
y+=+89 Same as before.
The second solution is: x = -10, y = 89 or (-10, 89}