Question

X + 2y = 5

3x + 5y = 14
Solve the system of equations.
(3, 1)
(2,3/2)
(7,-1)

Answer 1

The solution is (3, 1)

Explanation:

Use the method "elimination by addition and subtraction." Multiply all terms of the first equation by -3, obtaining

-3x - 6y = -15

and combine this result with the second equation:

-3x - 6y = -15

3x + 5y = 14

-----------------------

-y = -1, or y = 1.

Substituting this result, y = 1, into the first equation yields

x + 2(1) = 5, or x + 2 = 5, or x = 3.

The solution is (3, 1)

Answer 2

`x+2y = 5\\x = 5 -2y\\\\Substitute \ x \ in \ second \ equation \\\\3(5-2y) +5y = 14\\15 -6y +5y = 14\\-y = 14 -15\\-y = -1\\y = 1\\Substitute \ y = 1 \ in \ x = 5 -2y:\\ x = 5 -(2\cdot 1) = 5-2=3\\`

Option (3, 1)