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Text Solution

There are exactly 4 solutionsThere are exactly 2 solutionsThere is exactly 1 solution.There are no solutions

Answer :

CSolution :

The second equation of the system can be rewritten as y = 5x − 8. Substituting 5x − 8 for y in the first equation gives`5x − 8 = x^2 + 3x − 7`. This equation can be solved as shown below: <br> `x^2 + 3x -7 -5x+8=0` <br> `x^2-2x+1=0` <br> `(x-1)^2 =0` <br> x=1 <br> Substituting 1 for x in the equation y = 5x − 8 gives y = −3. Therefore, (1, −3) is the only solution to the system of equations. Choice A is incorrect. In the xy-plane, a parabola and a line can intersect at no more than two points. Since the graph of the first equation is a parabola and the graph of the second equation is a line, the system cannot have more than 2 solutions. Choice B is incorrect. There is a single ordered pair (x, y) that satisfies both equations of the system. Choice D is incorrect because the ordered pair (1, −3) satisfies both equations of the system. **What we already learned in previous class**

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