Solve Linear Equations

Solve Linear Equations Let us take a mathematical problem to indicate the necessary steps to solve the linear equations: Example 1: - 3x 2y = 2 (1) 7x + 3y = 43 (2) Instruction Method of solution a) From equation (1), express x in terms of y. likewise, from equation (2), express x in terms of y. From equation (1): 3x=2y+2 So, x=(2y+2)/3 (3) From equation (2) 7x=-3y+43 x= (-3y+43)/7 (4) b) Evaluate the values of x in (3) and (4) forming the equation in y. From equation (3) and (4), we get, (2y+2)/3=(-3y+43)/7 (5) c) Solve the linear equation (5) in y Simplifying, we get 14y+14=-9y+129 23y=115 y=5 d) Putting the values of y in (3) or (4), find the value of x Putting the value of y in equation (3) we get x=(2*5 +2)/3=4 e) Required solution of the two equations Therefore x=4 And y =5 Example 2: -7x 3y =31 (1) 9x 5y = 41 (2) Solution: - From equation (1) we get 7x = 31+3y x= (31+3y)/7 (3) Similarly from equation (2) we get, 9x = 41 + 5y x = (41 + 5y) / 9 (4) From equations (3) and (4) (31 + 3y) / 7 = (41 + 5y) /9 9(31 + 3y) = 7(41+5y) 279 +27y = 287+35 y 8y = -8 y = -1 Putting the value of y = -1 in equation (3) we get, x=(31-3)/7=28/7=4 Therefore x =4 and y = -1