If The Lines X+y+1=0 4x+3y+4=0

3 min read Jun 26, 2024
If The Lines X+y+1=0 4x+3y+4=0

Solving a System of Linear Equations: x+y+1=0 and 4x+3y+4=0

In this article, we will explore how to solve a system of linear equations, specifically the two equations x+y+1=0 and 4x+3y+4=0.

What are Linear Equations?

A linear equation is an equation in which the highest power of the variable (in this case, x and y) is 1. In other words, a linear equation can be written in the form:

ax + by + c = 0

where a, b, and c are constants, and x and y are variables.

The Given Equations

We are given two linear equations:

Equation 1: x + y + 1 = 0 Equation 2: 4x + 3y + 4 = 0

Our goal is to find the values of x and y that satisfy both equations.

Solving the System of Equations

There are several methods to solve a system of linear equations, including substitution, elimination, and graphing. Here, we will use the substitution method.

Step 1: Solve one of the equations for one variable

Let's solve Equation 1 for y:

y = -x - 1

Step 2: Substitute the expression into the other equation

Substitute y = -x - 1 into Equation 2:

4x + 3(-x - 1) + 4 = 0

Step 3: Simplify and solve for x

Simplify the equation:

4x - 3x - 3 + 4 = 0 x + 1 = 0 x = -1

Step 4: Substitute the value of x back into one of the original equations to find y

Substitute x = -1 into Equation 1:

y = -x - 1 y = -(-1) - 1 y = 1 - 1 y = 0

The Solution

Therefore, the solution to the system of linear equations is x = -1 and y = 0.

Conclusion

In this article, we have shown how to solve a system of linear equations using the substitution method. By following these steps, we were able to find the values of x and y that satisfy both equations.