A system of two linear equations in two variables is shown below. 4x+2y=8 y=3x-6 Joakim claims that there exists a matrix [} a&b c&d ] represents the system of linear equations. For the case where the claim is true, what must be the matrix [} a&b c&d ] A [} 4&2 1&3 ] B. [} 4&2 3&1 ] C. [} 4&2 1&-3 ] D. [} 4&2 -3&1 ]

Question

Answer 1

To determine which matrix represents the system of linear equations, we need to multiply the matrix by the vector

and see if it results in the vector

.Let's start by multiplying the matrix

by the vector

:

We want this to be equal to

, so we have the following system of equations:

Now let's compare these equations to the original system of linear equations:

We can see that the first equation matches the first equation in the original system, so we need to find the values of

,

, and

that satisfy the second equation.Substituting

into the second equation, we get:

Expanding and simplifying, we have:

Comparing this to the original second equation, we can see that

and

. Solving for

, we get

. Substituting this back into

, we find

.So the matrix that represents the system of linear equations is

, which corresponds to option D.

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