X+2y-4=0 2x+4y-12=0 By Substitution Method

2 min read Jun 26, 2024
X+2y-4=0 2x+4y-12=0 By Substitution Method

Solving Simultaneous Linear Equations by Substitution Method

In this article, we will solve a system of simultaneous linear equations using the substitution method. The given equations are:

Equation 1: x + 2y - 4 = 0 Equation 2: 2x + 4y - 12 = 0

Step 1: Rearrange Equation 1

Rearrange Equation 1 to isolate x:

x + 2y - 4 = 0 x = -2y + 4

Step 2: Substitute x into Equation 2

Substitute the expression of x from Equation 1 into Equation 2:

2x + 4y - 12 = 0 2(-2y + 4) + 4y - 12 = 0

Step 3: Simplify and Solve for y

Expand and simplify the equation:

-4y + 8 + 4y - 12 = 0 -4y + 4y + 8 - 12 = 0 0y - 4 = 0 y = 4/4 y = 1

Step 4: Substitute y back into Equation 1

Substitute the value of y back into Equation 1 to find the value of x:

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

Solution

The solution to the system of equations is:

x = 2 y = 1

Therefore, the point of intersection of the two lines is (2, 1).

Featured Posts