Hi
Can you help me to solve this simultaneous equation please?
\(\displaystyle \L 2x + y = 1 ....................1\)
\(\displaystyle \L \frac{1}{x} - \frac{1}{y} = 2.....................2\)
From (1)
\(\displaystyle \L y = 1 - 2x\)
Subst. into (2)
\(\displaystyle \L \frac{1}{x} - \frac{1}{{1 - 2x}} = 2\)
\(\displaystyle \L \frac{{1 - 2x - x}}{{x(1 - 2x)}} = 2\)
\(\displaystyle \L 1 - 2x - x = 2x(1 - 2x)\)
\(\displaystyle \L 1 - 2x - x = 2x - 4x^2\)
\(\displaystyle \L 4x^2 + 5x - 1 = 0\)
Using the quadratic formula:
\(\displaystyle \L x = \frac{{ - 5 \pm \sqrt {41} }}{8}\)
I do not think this answer is right. Please can you check it for me?
Thank you
Can you help me to solve this simultaneous equation please?
\(\displaystyle \L 2x + y = 1 ....................1\)
\(\displaystyle \L \frac{1}{x} - \frac{1}{y} = 2.....................2\)
From (1)
\(\displaystyle \L y = 1 - 2x\)
Subst. into (2)
\(\displaystyle \L \frac{1}{x} - \frac{1}{{1 - 2x}} = 2\)
\(\displaystyle \L \frac{{1 - 2x - x}}{{x(1 - 2x)}} = 2\)
\(\displaystyle \L 1 - 2x - x = 2x(1 - 2x)\)
\(\displaystyle \L 1 - 2x - x = 2x - 4x^2\)
\(\displaystyle \L 4x^2 + 5x - 1 = 0\)
Using the quadratic formula:
\(\displaystyle \L x = \frac{{ - 5 \pm \sqrt {41} }}{8}\)
I do not think this answer is right. Please can you check it for me?
Thank you