Question 1141180
start with:


2x-5y=7
3x+4y=2


multiply both sides of the first equation by 3 and multiply both sides of the second equation by 2 to get:


6x - 15y = 21
6x + 8y = 4


subtract the second equation from the first to get -23y = 17


solve for y to get y = -17/23


replace y with -17/23 in the first original equation to get 2x - 5y = 7 become 2x - 5 * -17/23 = 7.


multiply both sides of that equation by 23 to get 46x + 85 = 161


solve for x to get x = 76/46.


you have x = 76/46 and y = -17/23


replace x and y in both original equations with these values to get:


2x-5y=7 becomes 2 * 76/46 - 5 * -17/23 = 7.
multiply both sides of this equation by 46 to get 2 * 76 - 10 * -17 = 7 * 46.
simplify to get 152 + 170 = 322 which becomes 322 = 322 which is true.


3x+4y=2 becomes 3 * 76/46 + 4 * -17/23 = 2.
multiply both sides of this equation by 46 to get 3 * 76 + 8 * -17 = 2 * 46
simplify to get 228 - 136 = 92 which becomes 92 = 92 which is true.


both original equaitons are true when you replace x with 76/46 and y with -17/23, confirming the solution is correct.


your solution is x = 76/46 and y = -17/23.


x = 76/46 can be simplified to 38/23 while y remains simplified at -17/23.


those are your solutions.