Solve each of the following system of equations using pictur

Solve each of the following system of equations using pictures or algebra techniques. x + y = 13 x + y = 8 2x + 2y = 26 8x + 3y = 45 5x + 5 v = 45

Solution

a. x + y = 13...(1) and 2x + 2y = 26...(2)

On dividing both the sides of the 2nd equation by 2, we have x + y = 13. Thus, the 2nd equation is the same as the 1st equation. Now, we have 1 equation in 2 variables , which canot have a unique solution. There will be infinitely many solutions of the type x = t, y = 13-t where t is an arbitrary variable number.

b. x + y = 8...(1) and 5x + 5y = 45...(2)

On dividing both the sides of the 2nd equation by 5, we have x + y = 9. When we compare this with the 1st equation, we get 8 = 9, which is incorrect. Thus the given system of equations is inconsistent and does not have any solution.

c. x + y = 8...(1) and 8x + 3y = 45...(2)

From the 1st equation, we have y = 8 - x. Substituting this value of y in the 2nd equation, we get 8x + 3( 8 - x) = 45 or, 8x + 24 -3x = 45 or 5x = 45 -24 = 21. Therefore x = 21/5. Therefore y = 8 - x = 8 - 21/5 or, y = (40 -21)/5 = 19/5. We can verify the values x = 21/5 and y = 19/5 by substituting these values in the 2nd equation.