11. Solve the following system by elimination. Show work and explain each step. ) 3x+y=13 4x-3y=13 square

To solve the system of equations by elimination, we want to eliminate one of the variables by adding or subtracting the equations. In this case, we can eliminate the variable $y$ by multiplying the first equation by 3 and the second equation by 1, so that the coefficients of $y$ in both equations are equal.<br /><br />Multiplying the first equation by 3, we get:<br />$9x + 3y = 39$<br /><br />The second equation remains the same:<br />$4x - 3y = 13$<br /><br />Now, we can add the two equations together to eliminate the variable $y$:<br />$(9x + 3y) + (4x - 3y) = 39 + 13$<br />$13x = 52$<br /><br />Dividing both sides of the equation by 13, we get:<br />$x = 4$<br /><br />Now that we have the value of $x$, we can substitute it back into either of the original equations to solve for $y$. Let's use the first equation:<br />$3x + y = 13$<br />$3(4) + y = 13$<br />$12 + y = 13$<br /><br />Subtracting 12 from both sides of the equation, we get:<br />$y = 1$<br /><br />Therefore, the solution to the system of equations is $x = 4$ and $y = 1$.