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10x − 6y = 2

–2x + 3y = 14

1 answer

To solve the system of equations:

  1. \( 10x - 6y = 2 \) (Equation 1)
  2. \( -2x + 3y = 14 \) (Equation 2)

We can use the method of substitution or elimination. Here, I will use the elimination method to make it easier.

First, let's multiply Equation 2 by 2 to align the coefficients of \(x\):

\[ 2(-2x + 3y) = 2(14) \] \[ -4x + 6y = 28 \quad (Equation 3) \]

Now, we have:

  1. \( 10x - 6y = 2 \) (Equation 1)
  2. \( -4x + 6y = 28 \) (Equation 3)

Next, we can add Equation 1 and Equation 3:

\[ (10x - 6y) + (-4x + 6y) = 2 + 28 \] \[ 10x - 4x - 6y + 6y = 30 \] \[ 6x = 30 \]

Now, divide by 6:

\[ x = 5 \]

Now that we have \(x\), we can substitute it back into either equation to find \(y\). Let's use Equation 2:

\[ -2(5) + 3y = 14 \] \[ -10 + 3y = 14 \] \[ 3y = 14 + 10 \] \[ 3y = 24 \]

Now divide by 3:

\[ y = 8 \]

Thus, the solution to the system of equations is:

\[ (x, y) = (5, 8) \]