Question

Henri solved the system of equations below. What mistake did he make in his work?
3x + y = 6
x − 2y = 2

y = 6 − 3x
x − 2(6 − 3x) = 2
x − 12 + 6x = 2
7x − 12 = 2
+ 12 +12

x = 2

3(2) + y = 6
6 + y = 6
−6 −6
y = 0
He should have substituted 6 + 3x.
He combined like terms incorrectly. It should have been 5x instead of 7x.
He made a mistake in distributing −2.
He made no mistake.

Answer 1

he made no mistake

\[\begin{pmatrix}
3 & 1 & 6\\
1 & -2 & 2
\end{pmatrix}\to\begin{pmatrix}
1 & 0 & 2\\
0 & 1 & 0
\end{pmatrix}\]\(x=2\), \(y=0\)