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SSSSS [86.1K]
3 years ago
7

How many solutions does the equation 4x + 8 = −2 − 2 + 5x have?

Mathematics
1 answer:
joja [24]3 years ago
4 0
X=12  only has 1 solution
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x+y=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x^2-8x+16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

From equation (i), we have

x+y=4\\\\\Rightarrow y=4-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)

Substituting the value of y from equation (iii) in equation (ii), we get

y=x^2-8x+16\\\\\Rightarrow 4-x=x^2-8x+16\\\\\Rightarrow x^2-8x+16-4+x=0\\\\\Rightarrow x^2-7x+12=0\\\\\Rightarrow x^2-4x-3x+12=0\\\\\Rightarrow x(x-4)-3(x-4)=0\\\\\Rightarrow (x-3)(x-4)=0\\\\\Rightarrow x-3=0,~~~~~~~x-4=0\\\\\Rightarrow x=3,~4.

When, x = 3, then from (iii), we get

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And, when x = 4, then from (iii), we get

y=4-4=0.

Thus, the required solution of the given system is

(x, y) = (3, 1)  and  (4, 0).

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