4x Solve the system of equations using the elimination method. 5x-2y=12 3x+2y=36 Show your steps, and explain how you verify the solution.

To solve the system of equations using the elimination method, we can follow these steps:<br /><br />Step 1: Add the two equations together to eliminate the y variable.<br />$5x - 2y + 3x + 2y = 12 + 36$<br />$8x = 48$<br /><br />Step 2: Solve for x by dividing both sides of the equation by 8.<br />$x = \frac{48}{8}$<br />$x = 6$<br /><br />Step 3: Substitute the value of x into one of the original equations to solve for y.<br />Let's use the first equation: $5x - 2y = 12$<br />$5(6) - 2y = 12$<br />$30 - 2y = 12$<br />$-2y = 12 - 30$<br />$-2y = -18$<br />$y = \frac{-18}{-2}$<br />$y = 9$<br /><br />Therefore, the solution to the system of equations is $x = 6$ and $y = 9$.<br /><br />To verify the solution, we can substitute the values of x and y back into the original equations and check if both equations are satisfied.<br /><br />Substituting $x = 6$ and $y = 9$ into the first equation:<br />$5x - 2y = 12$<br />$5(6) - 2(9) = 12$<br />$30 - 18 = 12$<br />$12 = 12$ (True)<br /><br />Substituting $x = 6$ and $y = 9$ into the second equation:<br />$3x + 2y = 36$<br />$3(6) + 2(9) = 36$<br />$18 + 18 = 36$<br />$36 = 36$ (True)<br /><br />Since both equations are satisfied with the values of $x = 6$ and $y = 9$, the solution is correct.