Will make
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.

(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).

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.

what’s the question?