Answer:
Step-by-step explanation:
We can use the second expression to substitute for y in the first expression. Then we have ...
... 1/2x +11 = -7x^2 -9x +6
Subtracting the right side, we get
... 7x^2 +(9 1/2)x +5 = 0
Eliminating fractions by multiplying by 2, this is ...
... 14x^2 +19x +10 = 0
The discriminant of this equation will tell the number and kind of roots. For a=14, b=19, c=10, the discriminant is ...
... b^ -4ac = 19^2 -4·14·10 = 361 - 560 = -199
Since this value is negative, we know the two roots to the quadratic will be complex. There are no real solutions.
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The graph shows the two curves do not intersect, hence there are no values of x that will make the y-values match.
