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$y=x^{2}+3x-f$

$y-5x+8=0$

How many solutions are there to the system of equations above?

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$y=x^{2}+3x-f$

$y-5x+8=0$

How many solutions are there to the system of equations above?

","comment":{"@type":"Comment","text":"

Choice C is correct. 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:

$x^{2}+3x-7-5x+8=0$

$x^{2}-2x+1=0$

$(x-1)^{2}=0$

$x=1$.

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.

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$y=x^{2}+3x-f$

$y-5x+8=0$

How many solutions are there to the system of equations above?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

There are exactly 4 solutions.

"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

There are exactly 2 solutions.

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

There are no solutions.

"}],"acceptedAnswer":{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

There is exactly 1 solution.

","comment":{"@type":"Comment","text":"

"},"answerExplanation":{"@type":"Comment","text":"

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-168"}

$y=x^{2}+3x-f$$y-5x+8=0$How many solutions are there to the system of equations above?

$y=x^{2}+3x-f$$y-5x+8=0$How many solutions are there to the system of equations above?

$y=x^{2}+3x-f$$y-5x+8=0$How many solutions are there to the system of equations above?

$y=x^{2}+3x-f$

$y-5x+8=0$

How many solutions are there to the system of equations above?

$y=x^{2}+3x-f$

$y-5x+8=0$

How many solutions are there to the system of equations above?

$y=x^{2}+3x-f$

$y-5x+8=0$

How many solutions are there to the system of equations above?