Solve The System Of Equations Below.$ \begin{array}{l} 5x - 2y = 18 \\ 3x + 3y = 15 \end{array} $A. $(1, 4$\] B. $(-1, 4$\] C. $(4, 1$\] D. $(-4, 1$\]

Introduction

In mathematics, a system of linear equations is a set of two or more linear equations that are solved simultaneously to find the values of the variables. In this article, we will focus on solving a system of two linear equations with two variables. We will use the method of substitution and elimination to find the solution.

The System of Equations

The system of equations we will be solving is:

$$\begin{array}{l} 5x - 2y = 18 \\ 3x + 3y = 15 \end{array}$$

Step 1: Write Down the Equations

The first step in solving a system of linear equations is to write down the equations. In this case, we have two equations:

1. $5x - 2y = 18$
2. $3x + 3y = 15$

Step 2: Solve One of the Equations for One Variable

To solve the system of equations, we can use the method of substitution or elimination. In this case, we will use the elimination method. To do this, we need to solve one of the equations for one variable. Let's solve the first equation for $x$:

$$5x - 2y = 18$$

$$5x = 18 + 2y$$

$$x = \frac{18 + 2y}{5}$$

Step 3: Substitute the Expression for $x$ into the Other Equation

Now that we have an expression for $x$, we can substitute it into the other equation. Let's substitute the expression for $x$ into the second equation:

$$3x + 3y = 15$$

$$3\left(\frac{18 + 2y}{5}\right) + 3y = 15$$

Step 4: Simplify the Equation

Now that we have substituted the expression for $x$ into the other equation, we can simplify the equation:

$$\frac{54 + 6y}{5} + 3y = 15$$

$$54 + 6y + 15y = 75$$

$$21y = 21$$

Step 5: Solve for $y$

Now that we have simplified the equation, we can solve for $y$:

$$21y = 21$$

$$y = \frac{21}{21}$$

$$y = 1$$

Step 6: Substitute the Value of $y$ into One of the Original Equations

Now that we have found the value of $y$, we can substitute it into one of the original equations to find the value of $x$. Let's substitute the value of $y$ into the first equation:

$$5x - 2y = 18$$

$$5x - 2(1) = 18$$

$$5x - 2 = 18$$

Step 7: Solve for $x$

Now that we have substituted the value of $y$ into one of the original equations, we can solve for $x$:

$$5x - 2 = 18$$

$$5x = 20$$

$$x = \frac{20}{5}$$

$$x = 4$$

The Solution

The solution to the system of equations is:

$$x = 4$$

$$y = 1$$

Conclusion

In this article, we have solved a system of two linear equations with two variables using the method of substitution and elimination. We have found the values of $x$ and $y$ that satisfy both equations. The solution to the system of equations is $x = 4$ and $y = 1$.

Answer

The correct answer is:

$$

Introduction

In our previous article, we solved a system of two linear equations with two variables using the method of substitution and elimination. In this article, we will answer some common questions related to solving systems of linear equations.

Q: What is a system of linear equations?

A system of linear equations is a set of two or more linear equations that are solved simultaneously to find the values of the variables.

Q: What are the different methods for solving a system of linear equations?

There are two main methods for solving a system of linear equations: the substitution method and the elimination method.

Q: What is the substitution method?

The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation.

Q: What is the elimination method?

The elimination method involves adding or subtracting the equations to eliminate one of the variables.

Q: How do I choose which method to use?

You can choose which method to use based on the coefficients of the variables in the equations. If the coefficients of one variable are the same in both equations, you can use the elimination method. If the coefficients of one variable are different in both equations, you can use the substitution method.

Q: What if I have a system of three or more linear equations?

If you have a system of three or more linear equations, you can use the same methods as before, but you may need to use additional steps to solve the system.

Q: Can I use a graphing calculator to solve a system of linear equations?

Yes, you can use a graphing calculator to solve a system of linear equations. You can graph the equations on the calculator and find the point of intersection, which represents the solution to the system.

Q: What if I have a system of linear equations with no solution?

If you have a system of linear equations with no solution, it means that the equations are inconsistent and there is no value of the variables that satisfies both equations.

Q: What if I have a system of linear equations with infinitely many solutions?

If you have a system of linear equations with infinitely many solutions, it means that the equations are dependent and there are many values of the variables that satisfy both equations.

Q: Can I use a system of linear equations to model real-world problems?

Yes, you can use a system of linear equations to model real-world problems. For example, you can use a system of linear equations to model the cost of producing a product, the demand for a product, or the supply of a product.

Q: What are some common applications of systems of linear equations?

Some common applications of systems of linear equations include:

• Modeling the cost of producing a product
• Modeling the demand for a product
• Modeling the supply of a product
• Solving problems in physics and engineering
• Solving problems in economics and finance

Conclusion

In this article, we have answered some common questions related to solving systems of linear equations. We have discussed the different methods for solving a system of linear equations, how to choose which method to use, and some common applications of systems of linear equations.