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What Is the Solution to the Following System? mc016-1.jpg

In the field of mathematics, solving systems of equations is a fundamental concept that is widely applicable in various disciplines. One common method used to find the solution to simultaneous equations is substitution. In this article, we will explore the solution to a specific system of equations represented by mc016-1.jpg, and provide a step-by-step guide on how to solve it.

The given system of equations, mc016-1.jpg, consists of two linear equations with two variables, x and y. To find the solution, we will employ the substitution method. This technique involves substituting one equation into the other to eliminate one variable, resulting in an equation with a single variable, which can then be solved.

Step 1: Solve one equation for one variable

Let’s begin by solving the first equation, mc016-1a.jpg, for x:

mc016-1a.jpg

x = 2y + 4

Step 2: Substitute the expression for x into the second equation

Substitute the value of x from step 1 into the second equation, mc016-1b.jpg:

mc016-1b.jpg

4(2y + 4) + 3y = 14

Step 3: Simplify and solve for y

Expand the expression in parentheses and combine like terms:

8y + 16 + 3y = 14

11y + 16 = 14

11y = 14 – 16

11y = -2

y = -2/11

Step 4: Substitute the value of y into the first equation to find x

Using the value of y found in step 3, substitute it back into the first equation, mc016-1a.jpg:

x = 2(-2/11) + 4

x = -4/11 + 44/11

x = 40/11

Therefore, the solution to the given system of equations, mc016-1.jpg, is x = 40/11 and y = -2/11.

FAQs:

Q: What is a system of equations?

A: A system of equations is a set of two or more equations that share common variables.

Q: What is the substitution method?

A: The substitution method is a technique used to solve systems of equations by replacing one variable in terms of another and substituting it into the other equation.

Q: Can the substitution method be used for any system of equations?

A: The substitution method can be used for systems of linear equations, where all equations are linear (i.e., they involve variables raised to the power of 1).

Q: Are there other methods to solve systems of equations?

A: Yes, there are alternative methods such as the elimination method, graphing method, and matrix method. Each method has its own advantages and may be more suitable for different scenarios.

Q: How do I know if my solution is correct?

A: To verify the solution, substitute the values of x and y into the original equations, mc016-1.jpg. If the left side of each equation equals the right side, then the solution is correct.

Q: Can systems of equations have more than two variables?

A: Yes, systems of equations can involve any number of variables. However, the complexity of solving the system increases as the number of variables increases.

In conclusion, the solution to the system of equations mc016-1.jpg can be found using the substitution method. By substituting one equation into the other, we eliminate one variable and solve for the remaining variable. It is important to follow the steps carefully and double-check the solution by substituting it back into the original equations.

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