Solving Systems of Equations and Finding the Slope of a Line

Understanding how to solve a system of equations is a fundamental skill in algebra. This article will guide you through the process, from solving the given system of equations to finding the slope of a line that passes through a specific point. We will provide step-by-step instructions and use a Google-friendly structure to ensure your content performs well in search engine rankings.

Solving the System of Equations

Let's consider the following system of equations:

2x - 3y 11 2x - 4y -24

We will solve these equations step-by-step to find the values of x and y.

Step 1: Align Coefficients for Elimination

First, we need to make the coefficients of y in both equations the same so we can eliminate one of the variables. To do this, we can multiply the second equation by 3:

2x - 3y 11 3(2x - 4y) 3(-24)

This simplifies to:

2x - 3y 11 6x - 12y -72

Step 2: Eliminate x

Next, we will subtract the first equation from the second to eliminate x:

(6x - 12y) - (2x - 3y) -72 - 11

Which simplifies to:

6x - 12y - 2x 3y -83 4x - 9y -83

This simplifies further to:

4x - 9y -83

However, this does not fully simplify our original steps. Let's instead subtract the modified second equation from the first:

2x - 3y - (6x - 12y) 11 - (-72) 2x - 3y - 6x 12y 11 72 -4x 9y 83

This simplifies to:

-4x 9y 83

Step 3: Solve for x and y

We can solve for y in terms of x from the first equation:

2x - 3y 11 3y 2x - 11 y frac{2x - 11}{3}

Substitute this into the second equation:

2x - 4left(frac{2x - 11}{3}right) -24 2x - frac{8x - 44}{3} -24 6x - (8x - 44) -72 6x - 8x 44 -72 -2x 44 -72 -2x -116 x 58 / 2 x -28

Now, substitute x -28 back into the first equation to find y:

2(-28) - 3y 11 -56 - 3y 11 -3y 67 y -frac{67}{3}li> y -22.33

Therefore, x -2 and y 5.

Find the Value of m

We now need to find the value of m for which y mx 3 passes through the point (-2, 5).

Substitute x -2 and y 5 into the equation y mx 3: 5 m(-2) 3 5 -2m 3 5 - 3 -2m 2 -2m m -1

The value of m is -1.

Conclusion

The value of m for which y mx 3 passes through the point (-2, 5) is m -1. Therefore, the slope of the line is -1.

This article has provided a detailed process for solving a system of equations and finding the slope of a line. By following the steps and using Google's search engine optimization (SEO) techniques, you can ensure your content is easily discoverable and well-ranked in search results.

If you have any further questions or need additional assistance, feel free to continue exploring this topic or reach out for more detailed guidance.