Question

What is the solution to the system y = -4 x+2 and y = x-3

Answer 1

Answer:

To answer this question one can do either one of two methods one of which is elimination, or substitution:

Step-by-step explanation:

One these methods is two fold and that is one can be done with linear algebra which can represent the system of equations using a augmented matrix.

$4x+y=2\\-x+y=-3$

Now we can setup the Gauss-elimination using row echelon form:

$\left[\begin{array}{ccc}4&1&|+2\\-1&1&|-3\end{array}\right]$

The first thing we are gonna do is perform the indicated row operation

$\frac{1}4R_1+R_2$

Which gives you the following:

$\left[\begin{array}{ccc}4&1&|+2\\0&\frac{5}4&|-\frac{5}2\end{array}\right]$

Now we must perform another row operation

$4*R_2$

$\left[\begin{array}{ccc}4&1&|2\\ 0 &5&|-10\end{array}\right]$

Next row operation is the following:

$R_1-\frac{1}5R_2$

Which produces the following matrix

$\left[\begin{array}{ccc}4&0&|4\\0&5&|-10\end{array}\right]$

Then chain in these two row operations and you get the following:

$\frac{R_1}4\\\frac{R_2}5$

Which produces this matrix:

$\left[\begin{array}{ccc}1&0&1\\0&1&-2\end{array}\right]$

Which means the ordered pair is the following:

$(1,-2)$ is the solution