Answer
The error occured from step 2.
After correcting the error and solving,
x = -2
y = 4
Step-by-step explanation
The system of equations
2x + 2y = 4 ........ equation 1
x + 4y = 14 ........ equation 2
The solution in steps, using the substitution method as presented in the question will be checked one at a time to find the error
Step 1)
x = -4y + 14
Here x is made the subject of formula from equation 2.
Step 2)
2 (-4y +14) = 4
Here, the expression obtained for x in step 1 is substituted for x in eqn 1.
2x + 2y = 4
2 (-4y + 14) + 2y = 4
This is where the first error comes into play. The + 2y after substituting for x has been ignored here. This changes everything now.
Step 3)
- 8y + 28 = 4
After correcting the mistake in step 2, it should lead us to
2 (-4y + 14) + 2y = 4
-8y + 28 + 2y = 4
-6y + 28 = 4
Step 4)
- 8y = - 24
Following from correcting that error, if we subtract 28 from both sides, we will have
-6y + 28 = 4
-6y + 28 - 28 = 4 - 28
-6y = -24
Step 5)
y = -3
Further correcting the error will lead us to divide both sides by -6
-6y = -24
(-6y/-6) = (-24/-6)
y = 4
If y = 4, recall that x = -4y + 14
x = -4 (4) + 14
x = -16 + 14
x = -2
Hope this Helps!!!!