Question

Solve the system of equations by the addition method. 6x-2y -28 7x+7y=-14 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution is (Simplify your answer Type an ordered pair) There are infinitely many solutions B. O C. There is no solution.

Answer 1

Addition method is one of the methods to solve the system of linear equations. In addition method, two equations are ad to eliminate one of the variables. Now we have two equations - and in 0 6x-2y = -28 - FX +7Y = -14 - from (i) we get 3x-y=-14 [dividing both sides of from (W) we get, x+y=-2 [dividing both sides of i) by of] So, equation (it) and (iv) are the equivalent equations of equation ) and (ii) respectively. Now we will add the equation (in) and (in) 1. Adding Lits of both of the equations (15) and (iv) we get (3x-y) + (274) = 3x-y +x+y = 4x Adding Rts (14) we get, of both of the equations (1) and
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- 14+ (-2) = -14-2 = -16 Lits and so equating RHS we have, 4x=-16 or, x=-4 [ dividing both sides by - 47 0 (v) Hance we aree added see that to eliminate equations (1) the variable and y.

And there fore we have the value of a as [x = -4 Now by addition method we will try to eliminate the variable x and find the value firest multiply the equation (iv) og for this we -3. Then we get, - 3x-3y = 6 Adding (iii) and w and equating Lts and RHS we get (3x-y) + (-3%-3y) = -14+ 6 + 3x - y -38 - 5y = -9 =) - 4y = -8 y = 2 [ dividing both sides by -4] Hence eliminating a by adding (14) and ) We get the value of y as Ty=2) .: The solution is [x = -4 and y=2
so the correct choice is option A.. The solution is (-4,2)