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On a math test, Jun was asked to find the point(s) where the equations y = x2 + 10x – 6 & y = 7x – 2 intersect.

Jun’s solution is shown below.

Jun’s solution:
y = x2 + 10x – 6
y = 7x – 2
x2 + 10x – 6 = 7x – 2
x2 + 3x – 4 = 0
(x – 1) (x + 4) = 0
x = 1 or x = -4
The graphs intersect at (-4, 0) and (1, 0)

a) Is Jun’s solution correct? Explain why or why not.
b) If Jun’s solution is incorrect, show the correct work for this problem.

Answer:
 

Respuesta :

Answer:

B. juans solution is incorrect

Step-by-step explanation:

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Answer:

(a) Jun's work was correct as far as it went, but she didn't go far enough.

(b) (1, 5) and (-4, 30)

Step-by-step explanation:

y = x² + 10x – 6

y = 7x – 2

(a) Jun’s solution:

y = x² + 10x – 6

y = 7x – 2

x² + 10x – 6 = 7x – 2  

x² + 3x – 4 = 0

(x – 1)(x + 4) = 0

x = 1 or x = -4

Jun's work was correct to this point, but she didn't go far enough. She calculated the x-intercepts of the combined equation, not the values of x and y at which the two equations intersect.

Jun must calculate the value of y that corresponds to each value of x.

(b) The correct solution

Continue Jun's calculations

     y = 7x -2          y = 7x - 2

Set x = 1          Set x = -4

     y = 7 - 2          y = -28 -2

     y = 5               y = -30

The correct solutions are (1, 5) and (-4, 30).

The Figure below shows the graphs of each function with the intersection points at (1, 5) and (-4, 30).

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