What is the solution to the system of equations y+2x = 4 and 2y−6x = −12?

Solution:

Two linear equations in two or three variables solved together to find a common solution are called simultaneous linear equations.

Let's use the elimination method to solve the given equations.

Given:

y + 2x = 4 ------- (1)

2y − 6x = −12--------- (2)

Solving the two equations simultaneously,

We will multiply equation (1) by 2 and subtract it from equation (2) to eliminate the variable y.

(y + 2x = 4) × 2

⇒ 2y + 4x = 8

Subtracting this from equation (2) we get,

     2y - 6x = -12

     2y + 4x = 8

    (-)   (-)   =(-)

⇒ 0 + (-10x) = -20

⇒ x = 2

Using x = 2 in equation (1) we get,

y + 2 × 2 = 4 

⇒ y = 0

Thus, the value of x and y are 2 and 0 respectively.

---

What is the solution to the system of equations y+2x = 4 and 2y−6x = −12?

Summary:

The solution to the system of equations y + 2x = 4 and 2y − 6x = −12 are 2 and 0 respectively.