Blog: `2x - y + 2 = 0, 4x + y - 5 = 0` Solve the system by the method of substitution.

Saturday, August 24, 2013

Solve equation [2] for the variable y

$\displaystyle{y}=-{4}{x}+{5}$

Plug this in for variable y in equation [1]

$\displaystyle{2}{x}-{\left(-{4}{x}+{5}\right)}=-{2}$
$\displaystyle{6}{x}={3}$

Solve equation [1] for the variable x

$\displaystyle{6}{x}={3}$

$\displaystyle{x}=\frac{{1}}{{2}}$

By now we know this much :

$\displaystyle{x}=\frac{{1}}{{2}}$
$\displaystyle{y}=-{4}{x}+{5}$

Use the x value to solve for y

$\displaystyle{y}=-{4}{\left(\frac{{1}}{{2}}\right)}+{5}={3}$

Solution is $\displaystyle{\left(\frac{{1}}{{2}},{3}\right)}$

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