b) Use substitution method to solve the following simultaneous equations: 4x-3y=-3 4y-7x=-1

To solve the given system of equations using the substitution method, we can start by solving one of the equations for one variable in terms of the other variable. Let's solve the first equation for $x$ in terms of $y$:<br /><br />$4x - 3y = -3$<br /><br />Solving for $x$, we get:<br /><br />$4x = 3y - 3$<br /><br />$x = \frac{3y - 3}{4}$<br /><br />Now, we substitute this expression for $x$ into the second equation:<br /><br />$4y - 7x = -1$<br /><br />$4y - 7\left(\frac{3y - 3}{4}\right) = -1$<br /><br />Simplifying the equation, we get:<br /><br />$4y - \frac{21y - 21}{4} = -1$<br /><br />Multiplying through by 4 to clear the fraction, we have:<br /><br />$16y - 21y + 21 = -4$<br /><br />Combining like terms, we get:<br /><br />$-5y + 21 = -4$<br /><br />Solving for $y$, we get:<br /><br />$-5y = -25$<br /><br />$y = 5$<br /><br />Now that we have found the value of $y$, we can substitute it back into the expression for $x$ to find its value:<br /><br />$x = \frac{3(5) - 3}{4}$<br /><br />$x = \frac{15 - 3}{4}$<br /><br />$x = \frac{12}{4}$<br /><br />$x = 3$<br /><br />Therefore, the solution to the system of equations is $x = 3$ and $y = 5$.