1.) {5x+y=24x+y=4Use the linear combination method.A. (0, 2)B. (−2, 12)C. (−3, 17)D. (1, −8)2.)Solve.{2d−e=7d+e=5Use the linear combination method.A. There are infinitely many solutions.B. There is no solution.C. The solution is (4, 1).D. The solution is (3, −1) .3.)What is the solution of the system?5x−y=−21x+y=−34.)What is the solution of the system?−3x+9y=364x+12y=245.)What is the solution of the system of equations?7/2x−1/2y=9/23x−y=5

Answer:Ques 1)(-2,12)Ques 2)The solution is: (4,1)Ques 3)The solution is:(-4,1)Ques 4)The solution is: (-3, 3)Ques 5)The solution is: (1,-2)Step-by-step explanation:Ques 1)We have to solve the following system of equation using elimination method.{5x+y=24x+y=4we will subtract equation (2) from first to obtain:5x-4x=2-4x= -2Now on putting the value of x in first equation we obtain:5×(-2)+y=2-10+y=2y=2+10y=12Hence, the solution is:(-2,12)Ques 2)Now again we have to solve using linear combination method.{2d−e=7d+e=5we will add both the equations to get:2d+d=123d=12d=4and on putting the value of d in second equation we obtain:4+e=5e=5-4e=1Hence,C. The solution is (4, 1).Ques 3)5x−y=−21x+y=−3we will add both the equation to obtain:5x+x=-21-36x = -24x= -4and on putting the value of x in equation (2) we get:-4+y = -3y= -3+4y=1Hence, the solution is:(-4,1)Ques 4)−3x+9y=364x+12y=24we will divide first equation on both side by 3 and second equation on both side by 4 to obtain the system as:-x+3y=12x+3y=6on adding both the equations we get:3y+3y=12+6i.e. 6y=18i.e. y=3Hence on putting the value of y in one of the equation we obtain:x= -3Hence, the solution is:(-3,3)Ques 5)7/2x−1/2y=9/23x−y=5on multiplying both side of the equation by 2 we obtain:7x-y=9Now on subtracting second equation from this transformed equation we obtain:7x-3x=9-54x=4x=1Hence on putting the value of x in one of the equations we obtain the value of y as:y= -2Hence, the solution is:(1, -2)