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Find the solution of the system of equations.minus, 6, x, plus, 5, y, equals, 34−6x+5y=34minus, 6, x, minus, 10, y, equals, 4−6x−10y=4

Question

Find the solution of the system of equations.

The equations are:

  1. −6x+5y=34-6x + 5y = 34
  2. −6x−10y=4-6x - 10y = 4
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Solution

To solve the system of equations:

-6x + 5y = 34 -6x - 10y = 4

We can use the method of substitution or elimination. Here, we will use the elimination method since the coefficients of x in both equations are the same.

Step 1: Align the equations:

-6x + 5y = 34 -6x - 10y = 4

Step 2: Subtract the second equation from the first:

(-6x + 5y) - (-6x - 10y) = 34 - 4

This simplifies to:

15y = 30

Step 3: Solve for y:

y = 30 / 15 = 2

Step 4: Substitute y = 2 into the first equation:

-6x + 5(2) = 34 -6x + 10 = 34 -6x = 24 x = 24 / -6 = -4

So, the solution to the system of equations is x = -4, y = 2.

This problem has been solved

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