Answer:
Option A) multiply the top equation by 2 and the bottom equation by -3
Option D) To cancel the y's, multiply the top equation by -2.5.
Step-by-step explanation:
We are given the following equations in the question:
![3x+2y=17\\2x+5y=26](https://tex.z-dn.net/?f=3x%2B2y%3D17%5C%5C2x%2B5y%3D26)
We have to eliminate x from the equation in order to solve the equation.
Option A) multiply the top equation by 2 and the bottom equation by -3
![(3x+2y=17)\times 2\\ (2x+5y=26)\times -3\\\Rightarrow 6x + 4y = 34\\-6x-15y=-78\\\text{Adding equations we get}\\-11y = -44\\y = 4](https://tex.z-dn.net/?f=%283x%2B2y%3D17%29%5Ctimes%202%5C%5C%20%282x%2B5y%3D26%29%5Ctimes%20-3%5C%5C%5CRightarrow%206x%20%2B%204y%20%3D%2034%5C%5C-6x-15y%3D-78%5C%5C%5Ctext%7BAdding%20equations%20we%20get%7D%5C%5C-11y%20%3D%20-44%5C%5Cy%20%3D%204)
We have to eliminate y from the equation in order to solve the equation.
Option D) To cancel the y's, multiply the top equation by -2.5.
![(3x+2y=17)\times -2.5\\ (2x+5y=26)\times 1\\\Rightarrow -7.5x -5y = -42.5\\2x+5y=26\\\text{Adding equations we get}\\-5.5x = -16.5\\x = 3](https://tex.z-dn.net/?f=%283x%2B2y%3D17%29%5Ctimes%20-2.5%5C%5C%20%282x%2B5y%3D26%29%5Ctimes%201%5C%5C%5CRightarrow%20-7.5x%20-5y%20%3D%20-42.5%5C%5C2x%2B5y%3D26%5C%5C%5Ctext%7BAdding%20equations%20we%20get%7D%5C%5C-5.5x%20%3D%20-16.5%5C%5Cx%20%3D%203)