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Mathematics

OpenStudy (anonymous):

5x-y=19 and x-y=-1 substitution

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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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