Solve the simultaneous equation by substitution method [ 3 x-4 y=7 5 x-2 y=7 ]

To solve the system of equations using the substitution method, we can solve one equation for one variable and substitute it into the other equation. Let's solve the first equation for $x$:<br /><br />\[3x - 4y = 7\]<br /><br />\[3x = 4y + 7\]<br /><br />\[x = \frac{4y + 7}{3}\]<br /><br />Now, substitute this expression for $x$ into the second equation:<br /><br />\[5x - 2y = 7\]<br /><br />\[5\left(\frac{4y + 7}{3}\right) - 2y = 7\]<br /><br />Multiply both sides by 3 to eliminate the fraction:<br /><br />\[5(4y + 7) - 6y = 21\]<br /><br />\[20y + 35 - 6y = 21\]<br /><br />Combine like terms:<br /><br />\[14y + 35 = 21\]<br /><br />Subtract 35 from both sides:<br /><br />\[14y = -14\]<br /><br />Divide both sides by 14:<br /><br />\[y = -1\]<br /><br />Now that we have the value of $y$, we can substitute it back into the expression for $x$:<br /><br />\[x = \frac{4(-1) + 7}{3}\]<br /><br />\[x = \frac{-4 + 7}{3}\]<br /><br />\[x = \frac{3}{3}\]<br /><br />\[x = 1\]<br /><br />Therefore, the solution to the system of equations is $x = 1$ and $y = -1$.