Answer:
See below.
Step-by-step explanation:
So we have the system of equations:
[tex]3x-2y=21 \text{ and } y=2x-4[/tex]
The student took the following steps:
[tex]3x-2(2x-4)=21\\3x-4x-8=21\\-x-8=21\\-x=29\\x=-29\\y=2(-29)-4=-58-4=-62[/tex]
The student's mistake is in step 2. He/she distributed incorrectly. You are supposed to distribute the -2 to both terms, so it should be -4x plus 8, since -2 times -4 is positive 8. Fixing that mistake, we will have:
[tex]3x-2(2x-4)=21\\3x-4x+8=21 \\-x+8=21\\-x=13\\x=-13\\y=2(-13)-4=-26-4=-30[/tex]
Thus, the final answers should be (-13, -30).
