Solve the linear equation in a) Elimination Method b) Substitution Method                              2x – 3y = - 7 ---------①                             4x + 7y = 12----------②

To solve the given linear equations using the elimination method, we will eliminate one variable by adding or subtracting the equations. Let's solve it step by step:

a) Elimination Method: Step 1: Multiply equation (①) by 4 and equation (②) by 2 to make the coefficients of x in both equations equal: 8x - 12y = -28 ---------③ 8x + 14y = 24 ----------④

Step 2: Subtract equation (③) from equation (④) to eliminate x: (8x + 14y) - (8x - 12y) = 24 - (-28) 26y = 52 y = 52/26 y = 2

Step 3: Substitute the value of y into equation (①) to find the value of x: 2x - 3(2) = -7 2x - 6 = -7 2x = -7 + 6 2x = -1 x = -1/2

Therefore, the solution to the given linear equations using the elimination method is x = -1/2 and y = 2.

b) Substitution Method: Step 1: Solve equation (①) for x: 2x = 3y - 7 x = (3y - 7)/2

Step 2: Substitute the value of x from equation (①) into equation (②): 4((3y - 7)/2) + 7y = 12 2(3y - 7) + 7y = 12 6y - 14 + 7y = 12 13y - 14 = 12 13y = 12 + 14 13y = 26 y = 26/13 y = 2

Step 3: Substitute the value of y into equation (①) to find the value of x: 2x - 3(2) = -7 2x - 6 = -7 2x = -7 + 6 2x = -1 x = -1/2

Therefore, the solution to the given linear equations using the substitution method is x = -1/2 and y = 2.