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What is the solution to the system of linear equations represented by the matrix below?

[2 4] [x] = [6]

[1 2] [y] [3]

Ax= 3 , y= 0
Bx= 0 , y= 3/2
CThe system of equations has no solution
DThe system of equations has infinite solutions

Verified Answer :

Answer:

D. The system of equations has infinite solutions.

Step-by-step explanation:

Given system of equations,

\(\begin{bmatrix}2 & 4 \\ 1 & 2\end{bmatrix}.\begin{bmatrix}x\\ y\end{bmatrix}=\begin{bmatrix}6\\ 3\end{bmatrix}\)

\(\implies \begin{bmatrix}2x+4y\\ x+2y\end{bmatrix}=\begin{bmatrix}6\\ 3\end{bmatrix}\)

By comparing both sides,

We get,

2x + 4y = 6,

x + 2y = 3,

We know that a system \(a_1x+b_1y=c_1\), \(a_2x+b_2y=c_2\)

has a unique solution if,

\(\frac{a_1}{a_2} eq \frac{b_1}{b_2} eq \frac{c_1}{c_2}\)

No solution, if,

\(\frac{a_1}{a_2}=\frac{b_1}{b_2} eq \frac{c_1}{c_2}\)

Infinitely many solution if,

\(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)

Here,

\(\frac{2}{1}=\frac{4}{2}=\frac{6}{3}=2\)

Hence, the system of equation has infinite solutions.

Option D is correct.

correlltyson

Answer:

D ez tok test lol got right

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