SOLUTION: Here's the question and part of the solution. How many ordered pairs (x,y) satisfy this system of equations: x = 2y + 5 y = (2x-3)(x+9) Here's part of the solution: Step 1

Question 978100: Here's the question and part of the solution.
How many ordered pairs (x,y) satisfy this system of equations:
x = 2y + 5
y = (2x-3)(x+9)
Here's part of the solution:
Step 1. Substitute y in the 2nd equation into the first equation to get x = 2((2x-3)(x+9)) + 5
Step 2. The above = 4x^2 + 30x - 54
Step 3. The solution says this can be rewritten as: 4x^2 + 29x -54 = 0.
Here are my problems: What happened to the 5 on the end of the equation in Step 1? Where did the 29 come from in Step 3?
Thank you for any help?
Helen
Found 3 solutions by josgarithmetic, Boreal, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
, the substitution for x.

Find the solutions for y, which might be none, or one, or two of them.

I CHOSE to make the substitution for x instead of for y. You could just as well make the sub for y as you may have wanted. My view is that the subst for x is easier to use.

What you actually tried to do is tougher, and may be more work.
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
(2x-3)(x+9)= 2x^2+15x-27
2 times that is 4x^2+30x-54
but x=4x^2-30x-54] ;; original equation was x=2y+5
subtract x from both sides
0=4x^2+29x-49
You are right about the 5. That has to be carried through.
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Here's the question and part of the solution.
How many ordered pairs (x,y) satisfy this system of equations:
x = 2y + 5
y = (2x-3)(x+9)
Here's part of the solution:
Step 1. Substitute y in the 2nd equation into the first equation to get x = 2((2x-3)(x+9)) + 5
Step 2. The above = 4x^2 + 30x - 54
Step 3. The solution says this can be rewritten as: 4x^2 + 29x -54 = 0.
Here are my problems: What happened to the 5 on the end of the equation in Step 1? Where did the 29 come from in Step 3?
Thank you for any help?
Helen

x = 2y + 5 ----- eq (i)
y = (2x - 3)(x + 9) ----- eq (ii)
x = 2[(2x - 3)(x + 9)] + 5 ------- Substituting (2x - 3)(x + 9) for y in eq (i)

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