Solving systems of equations algebraically

Question

Terry tried to solve the system: x² +2x+2y=5 and 3x² -4x=3+y

Terry concluded that there are an infinite number of solutions to the system. At what number did terry make his first error, or we're none made?

 

1: x² +2x+2y=5

 

2: y= -1/2x² -x+5/2

 

3: x² +2x + 2(-1/2x² -x+5/2)=5

 

4: 5=5

Answer 1

Ok. So the error was that he solved the first equation for y which was fine, however, when he substituted it, (in step 3), he should have substituted it into the 2nd equation (3x² -4x=3+y).

 

Step 3 should be 3x² -4x=3+(-1/2x² -x+5/2)

 

 

 

 

Answer 2

Nope.

He solved the first equation for y.

THEN he plugged it into the first equation causing the identity.

 

He SHOULD have plugged it into the second equation:

 

3x^2 - 4x = 3 + (-1/2x^2 -x + 5/2)

 

3x^2 - 4x = 11/2 - 1/2x^2 - x <--- 3 + 5/2 = 6/2 + 5/2 = 11/2

 

6x^2 - 8x = 11 - x^2 - 2x  <--- multiplies everything by 2 to clear away the fraction

 

7x^2 - 6x - 11 = 0

 

x = [6 +or- sqrt( 36 - 4(7)(-11) )] / 14