Solve algebraically the simultaneous equations 2x+y=5 and 3x+y=7, for x and y.

Assign 2x+y=5 to be 'Equation 1,' and 3x+y=7 to be 'Equation 2.'The steps to solving for x and y are: 1.get rid of one variable (being either x or y) 2.solve for the other variable 3.substitute the now known value of that variable into the equation to solve for the other variable.For this question: 1.To get rid of one variable, we want the coefficient of it to be the same so that it will cancel out when the equations are either added or subtracted together. Notice in this question, in both equations, y has the coefficient of 1. To get rid of it, we want to subtract one equation from the other as 'y-y=0.' 2.We now subtract 'Equation 1' from 'Equation 2.' This gives us an equation of x=2. We do not need to do anything more to this as we have now solved for x. 3.We substitute x=2 back into either 'Equation 1' or 'Equation 2' to solve for y.Choosing 'Equation 1' gives:2(2)+y=54+y=5y=1We have solved the simultaneous equations and obtained values of x=2 and y=1. We can check these values by substituting them back into the equations. Eg. (using 'Equation 2') 3(2)+1=7; 7=7 so it is correct.