2 questions on simultaneous equations

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BigJoe6800
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I don’t really know how to approach either of this questions (except for the fact that I need to form simultaneous equations):

1) A rectangle has length L and width W. The perimeter of the rectangle is 17cm and the area is 15cm^2.
Find the possible lengths of W and L.

2) A circle has the equation x^2+y^2=25
Find the coordinates of the points of intersection of the circle with the straight line x+y = 1
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****Craic
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First one-> W+L=17
W.L=15

Rearrange W.L=15 and substitute into top one
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****Craic
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Second one-> rearrange both to get y=
Then put equal to each other and solve to get x coordinate.
Substitute x values into bottom equation to determine y coordinates.
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RDKGames
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(Original post by ShitCraic)
First one-> W+L=17
Not quite...

(Original post by BigJoe6800)
I don’t really know how to approach either of this questions (except for the fact that I need to form simultaneous equations):

1) A rectangle has length L and width W. The perimeter of the rectangle is 17cm and the area is 15cm^2.
Find the possible lengths of W and L.

2) A circle has the equation x^2+y^2=25
Find the coordinates of the points of intersection of the circle with the straight line x+y = 1
Q1: You should first of all write down the two simultaneous equations if you can. Then it's just a matter of simply rearranging one of them to make either L or W the subject, and then substituting that into the second equation and solving it.

Q2: The same approach as above
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BigJoe6800
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(Original post by ShitCraic)
Second one-> rearrange both to get y=
Then put equal to each other and solve to get x coordinate.
Substitute x values into bottom equation to determine y coordinates.
Thanks a lot!
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BigJoe6800
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(Original post by RDKGames)
Not quite...



Q1: You should first of all write down the two simultaneous equations if you can. Then it's just a matter of simply rearranging one of them to make either L or W the subject, and then substituting that into the second equation and solving it.

Q2: The same approach as above
Was it supposed to be 2W + 2L = 17 for Q1?
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RDKGames
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(Original post by BigJoe6800)
Was it supposed to be 2W + 2L = 17 for Q1?
Yes
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BrandonS03
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We know the general formula for a square as l x w right? So we can derive that L•W=15, We know that the general formula for the perimeter of a square is L+L+W+W or simply 2(L+W). So we can derive that 2(L + W)=17. Now you have two equations both with two unknown variables that are the same you can solve it. This same approach applies to your second question. But its more explicit. We know simultaneous equations are points on a graph where two functions intersect one another. That should be enough to help you solve that question.
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****Craic
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(Original post by RDKGames)
Yes
Oops 🤭 my fault sorry.
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