Do You Know How? In 4-6 solve each system using substitution. a y=(1)/(2)x+4 x-y=8 5. 3.25x-1.5y=1.25 13x-6y=10 6 y-0.8x=0.5 5y-2.5=4x

4. To solve the system of equations using substitution, we can substitute the expression for y from the first equation into the second equation:<br /><br />$y = \frac{1}{2}x + 4$<br /><br />$x - y = 8$<br /><br />Substituting the expression for y into the second equation, we get:<br /><br />$x - (\frac{1}{2}x + 4) = 8$<br /><br />Simplifying the equation, we have:<br /><br />$\frac{1}{2}x - 4 = 8$<br /><br />Adding 4 to both sides, we get:<br /><br />$\frac{1}{2}x = 12$<br /><br />Multiplying both sides by 2, we find:<br /><br />$x = 24$<br /><br />Now, we can substitute the value of x back into the first equation to find the value of y:<br /><br />$y = \frac{1}{2}(24) + 4$<br /><br />$y = 12 + 4$<br /><br />$y = 16$<br /><br />Therefore, the solution to the system of equations is $x = 24$ and $y = 16$.<br /><br />5. To solve the system of equations using substitution, we can solve one equation for one variable and then substitute it into the other equation.<br /><br />Let's solve the first equation for x:<br /><br />$3.25x - 1.5y = 1.25$<br /><br />$3.25x = 1.5y + 1.25$<br /><br />$x = \frac{1.5y + 1.25}{3.25}$<br /><br />Now, we can substitute this expression for x into the second equation:<br /><br />$13x - 6y = 10$<br /><br />$13(\frac{1.5y + 1.25}{3.25}) - 6y = 10$<br /><br />Simplifying the equation, we have:<br /><br />$\frac{13(1.5y + 1.25)}{3.25} - 6y = 10$<br /><br />$\frac{19.5y + 16.25}{3.25} - 6y = 10$<br /><br />Multiplying both sides by 3.25, we get:<br /><br />$19.5y + 16.25 - 19.5y = 32.5$<br /><br />$16.25 = 32.5$<br /><br />This equation is not true, which means there is no solution to the system of equations.<br /><br />6. To solve the system of equations using substitution, we can solve one equation for one variable and then substitute it into the other equation.<br /><br />Let's solve the first equation for y:<br /><br />$y - 0.8x = 0.5$<br /><br />$y = 0.8x + 0.5$<br /><br />Now, we can substitute this expression for y into the second equation:<br /><br />$5y - 2.5 = 4x$<br /><br />$5(0.8x + 0.5) - 2.5 = 4x$<br /><br />Simplifying the equation, we have:<br /><br />$4x + 2.5 - 2.5 = 4x$<br /><br />$4x = 4x$<br /><br />This equation is true for all values of x, which means the system of equations has infinitely many solutions.