High School

Solve the following system of equations, and indicate the values of [tex]x[/tex] and [tex]y[/tex]:

1. [tex]7x + 13y = 97.5[/tex]
2. [tex]14x + 12y = 97[/tex]

[tex]x =[/tex]
[tex]y =[/tex]

Answer :

The solution to the system of equations is x = 0.929 and y = 7.

To solve the system of equations:

7x + 13y = 97.5

14x + 12y = 97

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of elimination:

Multiply the first equation by 2 and the second equation by -1 to eliminate x:

14x + 26y = 195

-14x - 12y = -97

Adding these two equations, we get:

14x - 14x + 26y - 12y = 195 - 97

14y = 98

y = 98/14

y = 7

Now, substitute the value of y into one of the original equations, let's use the first equation:

7x + 13(7) = 97.5

7x + 91 = 97.5

7x = 97.5 - 91

7x = 6.5

x = 6.5/7

x = 0.9285714285714286

Therefore, the solution to the system of equations is x = 0.929 and y = 7.

For more details of system of equations :

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