Solve the system. (1) 5x + 2y = 5 (2) 3x - 4y = -23

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In summary, solving a system of equations involves finding the values of the variables that satisfy both equations. The first step is to choose a variable and solve for it using one of the equations, then substitute that value into the other equation to solve for the other variable. Both variables must be solved for to have a complete solution. Any equation in the system can be used to solve for a variable, but it may be more efficient to choose the one with a coefficient of 1. There are multiple methods for solving a system of equations, such as substitution, elimination, and graphing, and the best method may vary depending on the specific equations and personal preference.
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Explain the steps you would use to solve the following system of equations with the elimination method. Do not solve the system.

(1) 5x + 2y = 5

(2) 3x - 4y = -23
 
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(1) X 3 - (2) X 5 , you can get y. Similarly, you can get x.
 
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To solve this system using the elimination method, we need to eliminate one variable by adding or subtracting the two equations. In this case, we can eliminate the variable y by multiplying (1) by 2 and (2) by 4, giving us:

(1) 10x + 4y = 10

(2) 12x - 16y = -92

We can then subtract (1) from (2) to eliminate y:

(2) 12x - 16y = -92

- (1) 10x + 4y = 10

-----------------

2x = -102

Next, we can solve for x by dividing both sides by 2:

x = -51

Now, we can substitute this value of x into either of the original equations to solve for y. Let's use (1):

5(-51) + 2y = 5

-255 + 2y = 5

2y = 260

y = 130

Therefore, the solution to this system is (x,y) = (-51, 130).
 

What does it mean to "solve the system" of equations?

Solving a system of equations means finding the values of the variables that make both equations true at the same time.

What is the first step in solving this system of equations?

The first step is to choose one of the variables (x or y) and use one of the equations to solve for it. Once you have the value of that variable, you can substitute it into the other equation to solve for the other variable.

Do I have to solve for both variables?

Yes, in order to have a complete solution, you need to find the values of both x and y that make both equations true.

Can I use any equation to solve for a variable?

Yes, you can choose to solve for either x or y using either of the equations in the system. However, it may be more efficient to choose the equation that has the variable with a coefficient of 1.

Is there a specific method for solving this system of equations?

There are several methods for solving a system of equations, including substitution, elimination, and graphing. The best method to use may depend on the specific equations in the system and personal preference.

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