Vind the solution of the system of equations, 9x-7y=-5 -3x+7y=11 hnower Alemption of (-1,5)

To find the solution to the system of we can use the method of elimination or substitution. Here, we'll use the elimination method.<br /><br />Given:<br />\[ 9x - 7y = -5 \tag{1} \]<br />\[ -3x + 7y = 11 \tag{2} \]<br /><br />First, add the two equations to eliminate \( y \):<br /><br />\[ (9x - 7y) + (-3x + 7y) = -5 + 11 \]<br />\[ 9x - 3x = 6 \]<br />\[ 6x = 6 \]<br />\[ x = 1 \]<br /><br />Now, substitute \( x = 1 \) back into one of the original equations to solve for \( y \). We'll use equation (1):<br /><br />\[ 9(1) - 7y = -5 \]<br />\[ 9 - 7y = -5 \]<br />\[ -7y = -5 - 9 \]<br />\[ -7y = -14 \]<br />\[ y = 2 \]<br /><br />So, the solution to the system of equations is \( (1, 2) \).<br /><br />To verify, substitute \( x = 1 \) and \( y = 2 \) back into both original equations:<br /><br />For equation (1):<br />\[ 9(1) - 7(2) = 9 - 14 = -5 \]<br /><br />For equation (2):<br />\[ -3(1) + 7(2) = -3 + 14 = 11 \]<br /><br />Both equations are satisfied, confirming that the solution \( (1, 2) \) is correct.