Solve using eli mination. 10x-9y=-16 -6x+8y=20 square square D

To solve the system of equations using elimination, we want to eliminate one of the variables by making the coefficients of that variable in both equations equal (but opposite in sign). Let's eliminate \(x\) first.<br /><br />Given:<br />\[ 10x - 9y = -16 \]<br />\[ -6x + 8y = 20 \]<br /><br />First, we need to make the coefficients of \(x\) in both equations equal (but opposite in sign). We can do this by multiplying the first equation by 3 and the second equation by 5:<br /><br />\[ 3(10x - 9y) = 3(-16) \]<br />\[ 5(-6x + 8y) = 5(20) \]<br /><br />This gives us:<br />\[ 30x - 27y = -48 \]<br />\[ -30x + 40y = 100 \]<br /><br />Now, we add the two equations together to eliminate \(x\):<br /><br />\[ (30x - 27y) + (-30x + 40y) = -48 + 100 \]<br />\[ 30x - 30x - 27y + 40y = 52 \]<br />\[ 13y = 52 \]<br /><br />Solving for \(y\):<br />\[ y = \frac{52}{13} \]<br />\[ y = 4 \]<br /><br />Now that we have \(y = 4\), we can substitute it back into one of the original equations to solve for \(x\). Let's use the first\[ 9y = -16 \]<br />\[ 10x - 9(4) = -16 \]<br />\[ 10x - 36 = -16 \]<br />\[ 10x = -16 + 36 \]<br />\[ 10x = 20 \]<br />\[ x = \frac{20}{10} \]<br />\[ x = 2 \]<br /><br />So, the solution to the system of equations is:<br />\[ x = 2 \]<br />\[ y = 4 \]<br /><br />Therefore, the solution is:<br />\[ \boxed{(2, 4)} \]