Explain, in complete sentences, how you would use the substitution method to solve the following system of equations. Provide the solution to the system. 5x - y = -1 7x - 3y = 13
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First, solve one of the equations for x. Then substitute (emphasis on substitute) that expression into the other equation. Therefore, the second equation is in terms of y. Solve that equation for y and substitute back into the first to solve for x. Let's solve the first equation for y (it will be easier). It becomes \[y = 5x + 1\]Let's substitute this into the second equation. This yields\[7x -3(5x+1) = 13\] Expanding....\[7x - 15 x -3 = 13\]Combining like terms and adding three to both sides....\[-8x = 16\]Solving for x....\[x = -2\]Now let's plug this back into our expression for y\[y = 5(-2) + 1\]Therefore,
Oops. Therefore, \[y = -9 ~ and ~ x = -2\]
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