Question

The values of x and y that simultaneously satisfy the equations 2x + 3y = 5 and 7x - 4y = 3 are

• A. 0, 1
• B. 1, 0
• C. -1, 1
• D. 1, 1

Answer 1

Answer: (D)

1, 1

Equation I = 2x + 3y = 5
Equation II = 7x - 4y = 3
Multiplying first equation by 4 =
$\to$ 2x + 3y = 5
$\therefore$ (2x + 3y = 5) x (4)
= (8x + 12y = 20)......... (equation.III)
Now Multiplying second equation by 3 =
$\to$ 7x - 4y = 3
$\therefore$ (7x - 4y = 3) x (3)
= (21x - 12y = 9).......... (equation IV)
Now, Add Equation III with Equation IV.
$\to$ (8x + 12y = 20) + (21x - 12y = 9)
$\to$ (8x + 21x) + (12y - 12y) = (20 + 9)
$\to$ 29x + 0 = 29
$\to$ 29x = 29
$\to$ x = 29/29
$\to$ x = 1
We get : x = 1,
Now Putting x = 1 in Equation I,
$\to$ 2x + 3y = 5
$\to$ 2(1) + 3y = 5
$\to$ 2 + 3y = 5
$\to$ 3y = 5 - 2
$\to$ 3y = 3
$\to$ y = 3/3
$\to$ y = 1
So (x, y) = (1, 1)