Question

Describe the error that was made in solving the system by substitution, and explain how to solve the

problem correctly.
8x + 2y = -12
15x - y = 4

Step 1 5x - y = 4
-y = -5x +4
y = 5x - 4
Step 2 5x (5x - 4) = 4
5x-5x + 4 = 4
4=4

Answer 1

The mistake was in substituting terms incorrectly when using the substitution method. The correct approach is to solve one equation for one variable and substitute that into the other equation, then solve for each variable sequentially.

Step-by-step explanation:

The error in solving the system by substitution was incorrectly substituting the value from the first equation into the second equation and creating a new, nonsensical equation.

To solve the system correctly, you should first isolate y in the second equation to find y in terms of x.

Then, substitute this expression in place of y in the first equation to find the value of x.

Finally, substitute the value of x back into the equation for y to find the value of y.

Correct Steps:

1. Solve the second equation for y: 15x - y = 4 becomes y = 15x - 4.
2. Substitute y in the first equation: 8x + 2(15x - 4) = -12.
3. Solve for x: 38x - 8 = -12, then x = -1/19.
4. Substitute x back into the equation for y: y = 15(-1/19) - 4, then y = -19/19.