The values of x and y for the system of linear equations: y=2x-

korporasidn 2021-11-22 Answered
The values of x and y for the system of linear equations:
\(\displaystyle{y}={2}{x}-{4}\)
\(\displaystyle{y}^{{{2}}}={4}{x}\)

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Expert Answer

Rosemary McBride
Answered 2021-11-23 Author has 990 answers
Step 1
Putting the value of y from (1) in (2)
\(\displaystyle{\left({2}{x}-{4}\right)}^{{{2}}}={4}{x}\)
\(\displaystyle{4}{x}^{{{2}}}+{16}-{16}{x}={4}{x}\)
\(\displaystyle{4}{\left({x}^{{{2}}}+{4}-{4}{x}\right)}={4}{x}\)
\(\displaystyle{\left({\left({a}\pm{b}\right)}^{{{2}}}={a}^{{{2}}}+{b}^{{{2}}}\pm{2}{a}{b}\right)}\) \(\displaystyle{x}^{{{2}}}+{4}-{4}{x}={x}\)
\(\displaystyle{x}^{{{2}}}-{5}{x}+{4}={0}\)
\(\displaystyle{x}^{{{2}}}-{4}{x}-{x}+{4}={0}\)
\(\displaystyle{x}{\left({x}-{4}\right)}-{1}{\left({x}-{4}\right)}={0}\)
\(\displaystyle{\left({x}-{4}\right)}{\left({x}-{1}\right)}={0}\)
Either \(\displaystyle{x}-{4}={0}\) or \(\displaystyle{x}-{1}={0}\)
Either \(\displaystyle{x}={1}\) or \(\displaystyle{x}={4}\)
Putting the value of x in (2)
\(\displaystyle{y}^{{{2}}}={4}{\left({1}\right)}={4}\)
\(\displaystyle{y}=\pm{2}\)
\(\displaystyle{y}^{{{2}}}={4}{\left({4}\right)}={16}\)
\(\displaystyle{y}=\pm{4}\)
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