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To solve the system of equations using substitution:

1. Start with the given equations:
   \[
   x + 4y = 3
   \]
   \[
   2x - y = 4
   \]

2. Solve the first equation for \(x\):
   \[
   x = 3 - 4y
   \]

3. Substitute \(x = 3 - 4y\) into the second equation:
   \[
   2(3 - 4y) - y = 4
   \]
   \[
   6 - 8y - y = 4
   \]
   \[
   6 - 9y = 4
   \]
   \[
   -9y = 4 - 6
   \]
   \[
   -9y = -2
   \]
   \[
   y = \frac{2}{9}
   \]

4. Substitute \(y = \frac{2}{9}\) back into \(x = 3 - 4y\):
   \[
   x = 3 - 4\left(\frac{2}{9}\right)
   \]
   \[
   x = 3 - \frac{8}{9}
   \]
   \[
   x = \frac{27}{9} - \frac{8}{9}
   \]
   \[
   x = \frac{19}{9}
   \]

Thus, the solution is \(\left(\frac{19}{9}, \frac{2}{9}\right)\), which matches option (b).

Using the method of substitution to solve the system:
x + 4y = 3
2x - y = 4

Learn how to solve a system of linear equations using the substitution method. This example involves solving the equations x + 4y = 3 and 2x - y = 4 step by step. Perfect for students in Grades 8-10.

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