4x − y = −11 <span>2x + 3y = 5 lets multiply the second equation by -2 and add it to the first: </span><span> 4x − y = −11 </span>-4x - 6y = -10 ------------------ 0 - 7y = -21 y = -21/-7 y = 3 now we substitute this result in the first equation to find x: <span>4x − y = −11 </span>4x - 3 = -11 4x = -8 x = -8/4 x = 2 so the solution is y = 3 and x =2
4x − 9y = −21 <span>−10y = −30 </span>we solve for y <span>−10y = −30 </span>y = -30/-10 y = 3 and substitute in the first equation: <span>4x − 9y = −21 </span><span>4x − 9(3) = −21 </span>4x - 27 = -21 4x = 6 x = 6/4 = 3/2 so the solution is x = 3/2 and y = 3
4x + 3y = 5 <span>2y = −6 </span>we solve for y: <span>2y = −6 </span>y = -6/2 y = -3 we do substitute in the first equation: <span> 4x + 3y = 5 </span><span> 4x + 3(-3) = 5 </span>4x - 9 = 5 4x = 14 x = 14/4 x = 7/2 so the solution is x = 7/2 and y = -3
7x − 3y = −11 <span>9x = −6 </span>we solve for x: <span>9x = −6 </span>x = -6/9 x = -2/3 then we substitute in the first equation the result found: <span>7x − 3y = −11 </span><span>7(-2/3) − 3y = −11 </span>-14/3 - 3y = -11 we multiply by 3 to eliminate fractions: -14 - 9y = -33 9y = 19 y = 19/9 so the solution is x = -2/3 and <span>y = 19/9
</span>12x − 3y = −33 <span>14x = −28 </span>we solve for x: <span>14x = −28 </span>x = -28/14 x = -2 then we substitute in the first equation: <span>12x − 3y = −33 </span><span>12(-2) − 3y = −33 </span>-24 - 3y = -33 3y = 9 y = 3 then the solution is x = -2 and y = 3
