Solve using substitution. 7x+8y=-9 5x-4y=13 d square

To solve the system of equations using substitution, we can solve one equation for one variable and then substitute that expression into the other equation.<br /><br />Let's solve the first equation for $x$:<br />$7x + 8y = -9$<br />$7x = -9 - 8y$<br />$x = \frac{-9 - 8y}{7}$<br /><br />Now, substitute this expression for $x$ into the second equation:<br />$5x - 4y = 13$<br />$5\left(\frac{-9 - 8y}{7}\right) - 4y = 13$<br />$\frac{-45 - 40y}{7} - 4y = 13$<br />$-45 - 40y - 28y = 91$<br />$-68y = 136$<br />$y = -2$<br /><br />Now that we have the value of $y$, we can substitute it back into the expression for $x$:<br />$x = \frac{-9 - 8(-2)}{7}$<br />$x = \frac{-9 + 16}{7}$<br />$x = \frac{7}{7}$<br />$x = 1$<br /><br />Therefore, the solution to the system of equations is $x = 1$ and $y = -2$.