How do i solve simultaneous equations?

simulatneous equations are solved by eliminating one of the unknowns such as x or y. there are a number of ways to do this such as substitution or subtraction/addition. For this example we will use subtraction addition as i always found that the easier method at GCSE since it often avoids fractions.e.g. 2y=3x+12 and 3y=5x+14we need to choose one of the two unknowns to eliminate and then find their lowest common denominator. I will choose x, where the LCD is 15 (35=15). now we multiply the entire equation through in order that the number in front of x (called the coefficient) is 15. in the first equation, we multiply through by 5.(25)y=(35)x+(125)10y=15x+60in the second equation we multiply through by 3 like before(33)y=(53)x+(143)9y=15x+42now both the coefficients of x are 15 so we can subtract one equation from the other(10-9)y=(15-15)x+(60-42)y=0x+18y=18we now have the y value, since x is now zero. to find the x value all we need to do is go back to one of the first equations and put the value y=18 into the equation to resolve for x.(218)=3x+1236-12=3x24=3xx=8and thats everything. By making sure we can subtract one equation from another to eliminate one of the unkowns we can subsequently obtain both values. in this case, y=18 and x=8