Question

Solve by elimination

Answer 1

so, we will eliminate one of the variables, by multiplying one of the equations by "some number" that will be the opposite of the one below, say....  let's eliminate the "y", so if we multiply (-7y) * -2, we get +14y,  and 14y - 14y = 0, so let's use that.

$\bf \begin{array}{llll} -x~~-7y=~14& \times -2\implies &~~2x+14y=-28\\ -4x-14y=28&&-4x-14y=~~28\\ \cline{3-3} &&-2x~~~~~~~~=~~0 \end{array} \\\\\\ -2x=0\implies \boxed{x=0} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using that \underline{x} in the 1st equation}}{-(0)-7y=14}\implies y=\cfrac{14}{-7}\implies \boxed{y=-2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (0, -2)~\hfill$