Question

What is the solution to this system of equations?

x + 2 y = 4. 2 x minus 2 y = 5.
(3, Negative 5 and one-half)
(3, one-half)
no solution
infinitely many solutions

Answer 1

`\sf \left(3 , (1)/(2)\right)`

Explanation:

Solving system of linear equations:

x + 2y = 4 ----------------(I)

2x - 2y = 5 ---------------(II)

When we add the equations, y will be eliminated, and we obtain the value of 'x'.

(I) x + 2y = 4

(II) 2x - 2y = 5 {Add}

3x = 9

x = 9 ÷ 3

`\boxed{\bf x = 3}`

Substitute x = 3 in equation (I),

3 + 2y = 4

2y = 4

2y = 4 - 3

2y = 1

`y = (1)/(2)\\\\\boxed{\bf y = (1)/(2)}`

Answer:

`\bf \left(3 , (1)/(2) \right)`