Question

What is the solution set of the following system of equations?

5x - 3y - 10 = 0
x + y - 7 = 0

{(31/8, 25/8)}
{(25/8, 31/8)}
{(45/2, 31/2)}
{(31/2, 45/2)}

Answer 1

(31/8, 25/8)

Explanation:

We can do this using the Elimination Method.

Try eliminating y

(5x - 3y - 10 = 0 )

3* (x + y - 7) = 3* 0

3x + 3y - 21 = 0

Add the two equations now.

5x - 3y - 10 + 3x + 3y - 21 = 0 + 0

5x + 3x - 3y + 3y - 10 - 21 = 0

8x -31 = 0

8x = 31

x = 31/8

Next we find y by plugging in for x in x + y - 7 = 0

(31/8) + y - 7 =0

y = 7 - 31/8

y = 56/8 - 31/8

y = 25/8