Solve using substitution.

8x + 4y = 4
4x + y = 11

1 answer

To solve the system of equations using substitution, we first need to express one variable in terms of the other from one of the equations.

We start with the second equation:

\[ 4x + y = 11 \]

We can solve for \( y \):

\[ y = 11 - 4x \]

Now we can substitute this expression for \( y \) into the first equation:

\[ 8x + 4y = 4 \]

Substituting \( y \):

\[ 8x + 4(11 - 4x) = 4 \]

Now, simplify the equation:

\[ 8x + 44 - 16x = 4 \]

Combine like terms:

\[ -8x + 44 = 4 \]

Next, isolate \( x \):

\[ -8x = 4 - 44 \] \[ -8x = -40 \]

Now, divide by -8:

\[ x = 5 \]

Now that we have \( x \), we can substitute it back into the expression we found for \( y \):

\[ y = 11 - 4x \] \[ y = 11 - 4(5) \] \[ y = 11 - 20 \] \[ y = -9 \]

Thus, the solution to the system of equations is:

\[ \boxed{(5, -9)} \]

Verification:

We can verify our solution by substituting \( (5, -9) \) back into the original equations.

  1. For the first equation \( 8x + 4y = 4 \): \[ 8(5) + 4(-9) = 40 - 36 = 4 \quad \text{(True)} \]

  2. For the second equation \( 4x + y = 11 \): \[ 4(5) + (-9) = 20 - 9 = 11 \quad \text{(True)} \]

Both equations are satisfied, confirming that the solution \( (5, -9) \) is correct.

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