Solving the following system of equations

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The discussion focuses on solving a system of equations: 2x + 3y = 7 and 2x^2 - 3y^2 = -25. The first equation is linear, while the second is quadratic. The solution process involves isolating y in the first equation and substituting it into the second equation, leading to a quadratic equation in x. Participants emphasize using the quadratic formula to find x values, which can then be used to determine corresponding y values. The textbook solution set includes the pairs {(-1,3), (-13,11)}.
Spensy
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2x+3y = 7, -> equation1
2x^2-3y^2 = -25; -> equation2

first of all tell me the type of equations

first i solve for y equation 1

y = (-2x +7)/3

now what should i do ?
 
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Now plug that expression for y into equation 2 and solve for x. It will be a quadratic equation for x, so you will need the quadratic formula.
 
please i need more help can any 1 solve this equations my textbook has a solution set
{(-1,3),(-13,11)}

please help me I'd be thankful to you.
 
Spensy said:
2x+3y = 7, -> equation1
2x^2-3y^2 = -25; -> equation2

first of all tell me the type of equations

first i solve for y equation 1

y = (-2x +7)/3

now what should i do ?

So if y = (7-2x)/3, what is 3y2?
 
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