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Solve the following system of linear equations by addition. Indicate whether the given system of linear equations has one solution, hasno solution, or has an infinite number of solutions. If the system has one solution, find the solution.1.5x - 1.5y = 10.54.5.x - 4.5y = 31.5

Solve the following system of linear equations by addition. Indicate whether the given-example-1
User OlavT
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1 Answer

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Answer:

The given system

Explanations:

Given the system of equations as shown:

1.5x - 1.5y = 10.5____________ 1

4.5.x - 4.5y = 31.5 ___________2

Multiply equations 1 and 2 through by 10

15x - 15y = 105 _________________3 * 3

45x - 45y = 315 _________________4

Multiply equation 3 by 3 and subtract from equation 4

45x - 45y = 315 _________________3

45x - 45y = 315 _________________4

Since both expressions are the same, we can solve just one of the equations as shown;

45x - 45y = 315

Divide through by 45

x - y = 7

Let x = t where "t" is any real number

-y = -x + 7

y = x - 7

Substitute x = t into the expression for y to have;

y = t - 7

Hence the solution to the system of equations is (t, t-7)

Since the value of "t" can be any real number, hence the system of equations of an infinite number of solutions

User Mustafa
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