Solve the following system of equations by the substitution method. 8x=2y+5 3x=y+7 What is the solution set? (-41/2,-9/2) varnothing (-9/2,-41/2)

To solve the system of equations by the substitution method, we can start by solving one equation for one variable and then substituting that expression into the other equation.<br /><br />Let's solve the second equation for y:<br />$3x = y + 7$<br />$y = 3x - 7$<br /><br />Now, we can substitute this expression for y into the first equation:<br />$8x = 2(3x - 7) + 5$<br />$8x = 6x - 14 + 5$<br />$8x = 6x - 9$<br />$2x = -9$<br />$x = -\frac{9}{2}$<br /><br />Now that we have the value of x, we can substitute it back into the expression for y:<br />$y = 3(-\frac{9}{2}) - 7$<br />$y = -\frac{27}{2} - 7$<br />$y = -\frac{27}{2} - \frac{14}{2}$<br />$y = -\frac{41}{2}$<br /><br />Therefore, the solution set is $\{ (-\frac{9}{2}, -\frac{41}{2}) \}$.