Question

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

Answer 1

{x,y} = {3,1}

Explanation:

// Solve equation [1] for the variable x

[1] x = -2y + 5

// Plug this in for variable x in equation [2]

[2] 3•(-2y+5) + 5y = 14

[2] - y = -1

// Solve equation [2] for the variable y

[2] y = 1

// By now we know this much :

x = -2y+5

y = 1

// Use the y value to solve for x

x = -2(1)+5 = 3

Solution :

{x,y} = {3,1}

Answer 2

For this case we have the following system of equations:

`x + 2y = 5\\3x + 5y = 14`

To solve, we multiply the first equation by -3:

`-3x-6y = -15`

We add the equations:

`-3x + 3x-6y + 5y = 14-15\\-y = -1\\y = 1`

We look for the value of the variable "x":

`x + 2 (1) = 5\\x + 2 = 5\\x = 5-2\\x = 3`

Thus, the solution of the system is (3,1)

Answer:

(3,1)