Solve the system of equations.
x + 3y = 5
-x + 6y = 4
a) x = 1, y = 2
b) x = 2, y = 1
c) x = 1, y = 1
d) x = 0, y = 2

Option (b) is correct.

The solution of given system of linear equations is x= 2 and y = 1.

Step-by-step explanation:

Given : System of linear equations

x + 3y = 5

-x + 6y = 4

We have to solve the given system of linear equations.

Consider  the given system of linear equations.

x + 3y = 5   (1)

-x + 6y = 4 (2)

We will sole the system using elimination method.

Add both equation (1) and (2) and eliminate x , we have,

⇒ x + 3y + (-x + 6y) = 5 + 4

Simplify, we have,

⇒ 3y + 6y = 9

⇒ 9y = 9

Divide both side by 9, we have,

⇒ y = 1

Put y = 1 in equation (1) and solve for x, we have,

(1) ⇒ x + 3(1) = 5

⇒ x = 5 - 3

⇒ x = 2

Thus, the solution of given system of linear equations is x= 2 and y = 1.

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step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .