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VikaD [51]
3 years ago
15

How do I use the substitution method to find the point of intersection of

Mathematics
1 answer:
Goshia [24]3 years ago
7 0
To substitute, solve for one variable and then plug it into the other equation you have. In this problem, y is already solved for on the top equation (y=x+2), so you just stuff it into the second equation.

y = x + 2
3y = 4x - 2

3(x + 2) = 4x - 2
3x + 6 = 4x - 2
-x = -8
x = 8
y = x + 2 = 8 + 2 = 10

solution:
x = 8 
y = 10

hope this helps!! :)
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\displaystyle\\\\\frac{2}{x-2}+\frac{7}{x^2-4}=\frac{5}{x}\\\\\frac{^{x+2)}2~~~~~}{x-2}+\frac{7}{(x-2)(x+2)}=\frac{5}{x}\\\\\frac{2(x+2)}{(x-2)(x+2)}+\frac{7}{(x-2)(x+2)}=\frac{5}{x}\\\\\frac{2x+4+7}{x^2-4}=\frac{5}{x}\\\\\frac{2x+11}{x^2-4}=\frac{5}{x}\\\\5(x^2-4)=x(2x+11)\\\\5x^2-20=2x^2+11x\\\\5x^2-2x^2 -11x-20=0


\displaystyle\\3x^2-11x-20=0\\\\x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{11\pm\sqrt{121+4\cdot3\cdot20}}{2\cdot3}=\\\\=\frac{11\pm\sqrt{121+240}}{6}=\frac{11\pm\sqrt{361 }}{6}=\frac{11\pm19}{6}\\\\x_1=\frac{11-19}{6}=\frac{-8}{6}\\\\\boxed{\bf x_1=-\frac{4}{3}}\\\\x_2=\frac{11+19}{6}=\frac{30}{6}\\\\\boxed{\bf x_2=5}




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Step-by-step explanation:

You did not finish your question i dont think. 22 DOES round down to 20 though.

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