Solve the simultaneous equations x - 2y = 5 and 5x + 4y = 11

We can solve simultaneous equations one of two ways. We can either substitute one equation into the other or we can eliminate one of the unknowns only leaving us one to deal with. I will explain both methods as one you may find one easier to grasp than the other. Firstly, we want to make the coefficients in front of one of the unknowns the same. In this case it is easier for us to multiply the first equation by 2 to make the coefficients in front of the y’s both 4. This would now make the first equation 2x – 4y = 10. We can now add the two equations together to give the single equation of 7x =21 due to the y’s cancelling out. This equation can then be solved easily to give x=3 which can then be put back into one of the equations to find y = -1Another method is the substitution method. The first equation can be rearranged to x = 5 + 2y and then substituted into the second equation in place of the x giving 5(5 +2y) + 4y = 11. These brackets can then be expanded and the equation simplified to 14y = -14 giving y = -1. Y can then be input back into one og the equations to find x = 3.