Solve usin g elimin ation. 10x+7y=-9 8x+2y=-18 square square

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. In this case, we can eliminate $y$ by multiplying the second equation by $-7$ and adding it to the first equation.<br /><br />Multiplying the second equation by $-7$ gives:<br />$-7(8x+2y)=-7(-18)$<br />$-56x-14y=126$<br /><br />Now, we can add this equation to the first equation:<br />$10x+7y=-9$<br />$-56x-14y=126$<br /><br />Adding these equations gives:<br />$-46x=-183$<br /><br />Dividing both sides by $-46$ gives:<br />$x=4$<br /><br />Now that we have found 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 />$10x+7y=-9$<br />$10(4)+7y=-9$<br />$40+7y=-9$<br />$7y=-49$<br />$y=-7$<br /><br />Therefore, the solution to the system of equations is $x=4$ and $y=-7$.