Question

Error Analysis Identify and correct the error shown in finding the solution of:

3x – 4y = 14
x + y = 7
using substitution.

Answer 1

The error in solving the system of equations via substitution can be corrected by accurately solving one equation for a variable and substituting this into the other, then solving for the remaining variable.

Step-by-step explanation:

The student is asking for an error analysis in solving the system of equations:
3x – 4y = 14
4x + y = 7
using the substitution method. From the information provided, it seems there is a confusion in substituting values and solving the resultant equations. To solve using substitution, you usually solve one equation for one variable and then substitute that expression into the other equation. Here are the correct steps:

1. Solve the second equation for y: y = 7 – 4x.
2. Substitute the expression for y from step 1 into the first equation:
   3x - 4(7 - 4x) = 14.
3. Solve for x: 3x - 28 + 16x = 14, which simplifies to 19x = 42, so x = 42 / 19.
4. Substitute the value of x back into y = 7 – 4x to find the value of y.

By following these steps, you can solve the system of equations correctly.