Question

Which matrix equation represents the system of equations?
[4x - 2y = -7
3y = 5

Answer 1

The fourth one is the correct answer.

0 must come before 3 in the matrix, so that x will be multiplied with 0.

Answer 2

Therefore, the matrix equation represents the system of equations

4x - 2y = -7

0x + 3y = 5 is given by

$\left[\begin{array}{ccc}4&-2\\0&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}-7\\5\end{array}\right]$.

How to write a system of linear equations in matrix form?

Three easy steps must be taken in order to express any system of linear equations in matrix form:

1. First, create a single matrix with all the coefficients. An acronym for this is a coefficient matrix.

2. Multiply this matrix by the system setup variables in a different matrix. The variable matrix is another name for this.

3. In another matrix, place the solutions on the other side of the equal sign. The answer matrix is another name for this.

How to solve this problem?

Given system of linear equations:

4x - 2y = -7

0x + 3y = 5

The coefficient matrix is $\left[\begin{array}{ccc}4&-2\\0&3\end{array}\right]$.

The variable matrix is $\left[\begin{array}{ccc}x\\y\end{array}\right]$.

[ Since $\left[\begin{array}{ccc}4&-2\\0&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}4x-2y\\0x+3y\end{array}\right]$ ]

The answer matrix is $\left[\begin{array}{ccc}-7\\5\end{array}\right]$.

Therefore, the matrix equation represents the system of equations

4x - 2y = -7

0x + 3y = 5 is given by

$\left[\begin{array}{ccc}4&-2\\0&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}-7\\5\end{array}\right]$. So, the last option is correct.

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