3x+2y=12 ; 5x+3y=19

3x+2y=12 (1) /// 5x+3y=19 (2) /// . (1) x 3---(2) x -2 /// 9x+6y=36///-10x-6y=-38///x+0=-2/// x=2///y=5(2)+3y=19///y=9/3 = 3-///////--> x=2y=3first, we need to make one of the two terms (x or y) of the same value. to do this one or both equations must be multiplied by a number but bear in mind, the entire equation has to be multiplied to keep the right hand side equal to the left hand side. in this, if we multiply the 1st eq/ by 3 and the 2nd by -2, we get 6y and -6y. when these 2 are added they eliminate each other and in the equation we are only left with x to deal with. now we add all the other terms as well. 9x+(-10x) and 36+(-38), the answers for this are -x and -2 respectively. this shows that x=2. we now plug in this value of x in either one of our equations to get to y, which happens to be 3.