Question

If x+2y=10, 2x+4=11
then find
the
value of x+y
without actually
solving for x and y​

Answer 1

Step-by-step explanation:

Equation 1: x + 2y = 5

Equation 2: -10 + 4y = -2x

Equation 1, Multiplied by 2: 2x + 4y = 10

Equation 1, Multiplied by 2: 2x + 4y - 10 = 10 - 10

Equation 1, Multiplied by 2: 2x + 4y - 10 = 0

Equation 1, Multiplied by 2: 2x - 2x + 4y - 10 = 0 - 2x

Equation 1, Multiplied by 2: 4y - 10 = - 2x

Equation 1, Multiplied by 2: - 10 + 4y = - 2x

Notice that Equation 1 = Equation 2

One Solution

Equation 1: x - y = -10

Equation 2: 2x + 3y = 15

Equation 1, Rearranged: y = x + 10

Equation 1 Substituted into 2: 2x + 3(x + 10) = 15

Equation 1 Substituted into 2: 2x + 3x + 30 = 15

Equation 1 Substituted into 2: 5x + 30 = 15

Equation 1 Substituted into 2: 5x + 30 - 30 = 15 - 30

Equation 1 Substituted into 2: 5x = -15

Equation 1 Substituted into 2: x = -3

Equation 1, Solve for Y: 2(-3) + 3(y) = 15

Equation 1, Solve for Y: -6 + 3y = 15

Equation 1, Solve for Y: 3y = 21

Equation 1, Solve for Y: y = 7

Solution: x = -3, y = 7