Mathematics 46 Online OpenStudy (anonymous):

5x-y=19 and x-y=-1 substitution OpenStudy (shadowfiend):

Assuming you want to solve for x and y: The easiest place to start is $$x - y = -1$$. You can isolate $$x$$ by moving $$y$$ to the right: $$x = -1 + y = y - 1$$. Then, you can substitute for x in $$5x - y = 19$$: \begin{align} 5x - y &= 19\\ 5(y - 1) - y &= 19\\ 5y - 5 - y &= 19\\ 4y - 5 &= 19\\ 4y &= 24\\ y &= 6 \end{align} Now that you've determined the value of $$y$$, you can plug into the first equation to get the value of $$x$$: $x = y - 1 = 6 - 1 = 5$ You can then double-check that both of the equations are valid by plugging in the two values you just found for $$x$$ and $$y$$: $5 - 6 = -1$ $5\cdot 5 - 6 = 25 - 6 = 19$

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