A curve with equation y = x^2 + 2x + 3 crosses a straight line with equation y = x+9 in two places. Find the coordinates of the
1 answer:
Got you fam or whatever people say....
We have equation 1 and 2
1.
2.
Because equation 2 is simple and isn't quadtratic, we will insert 2 into 1,
Then factor
x² +x -6=0
(x+3)(x-2)=0
x= -3, 2
Then using the values of x insert into either equation 1 or 2 to find y. I'm doing 2 because I'm lazy
y= x+9
when x=-3
y=x+9
= -3+9
= 6
(-3,6)
when x =2
y=x+9
= 2+9
= 11
(2,11)
Hence the co-ordinates are (2,11) and (-3,6)
We have equation 1 and 2
1.
2.
Because equation 2 is simple and isn't quadtratic, we will insert 2 into 1,
Then factor
x² +x -6=0
(x+3)(x-2)=0
x= -3, 2
Then using the values of x insert into either equation 1 or 2 to find y. I'm doing 2 because I'm lazy
y= x+9
when x=-3
y=x+9
= -3+9
= 6
(-3,6)
when x =2
y=x+9
= 2+9
= 11
(2,11)
Hence the co-ordinates are (2,11) and (-3,6)
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The graph that shows the solution to the system of inequalities is: C (see the image attached below).
<h3>How to Determine the Graph of the Solution to a System of Inequalities?</h3>Given the following systems of inequalities:
y < -1/3x + 1
y ≤ 2x - 3
Below are the features of the graph that represents a solution to the system of inequalities:
- The boundary line of y < -1/3x + 1 would be a dashed line and the shaded area would be below it, because of the inequality sign, "<".
- The boundary lines of y ≤ 2x - 3 would be a solid line and the shaded area would be below it, because of the inequality sign, "≤".
- The slope of the shaded line that represents y < -1/3x + 1, would be -1/3, and the line would be a decreasing line which intersects the y-axis at 1.
- The slope of the line that represents y ≤ 2x - 3, would be 2, and the line would also be an increasing line that intersects the y-axis at -3.
Therefore, the graph that shows the solution to the system of inequalities is: C (see the image attached below).
Learn more about the graph of the system of inequalities on:
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