Question

Use an augmented matrix to solve the system. What is the Value of x and y?

Answer 1

QUESTION 1

The given equations are;

$x+y=5$

and

$3x-y=-1$

The augmented matrix is  

$\left[\begin{array}{ccc}1&1&|5\\3&-1&\:\:\:\:\:|-1\end{array}\right]$

$-3R_1+R_2\rightarrow R_2$

$\left[\begin{array}{ccc}1&1&|5\\0&-4&\:\:\:\:\:|-16\end{array}\right]$

$-\frac{1}{4} R_2\rightarrow R_2$

$\left[\begin{array}{ccc}1&1&|5\\0&1&|4\end{array}\right]$

$R_1-R_2\rightarrow R_1$

$\left[\begin{array}{ccc}1&0&|1\\0&1&|4\end{array}\right]$

This implies that $x=1$ and $y=4$

The correct answer is A(1,4).

QUESTION 2

To convert a linear equation into an augmented matrix we need to write the equation in the form;

$ax+by=c$

This is referred to as the standard form.

The correct answer is D.

QUESTION 3

When we write a system of equation as an augmented matrix, we use a straight line to separate the coefficient matrix from the constant matrix just like how the equal sign separates the variables from the constants in the standard form.

The straight line represents the equal sign.

The correct answer is C

Answer 2

D,a,a
Hope it helps
And right..