Question

1)A System of equations is shown below . What is the solution to the system of equations? 5x+2y=-15 2x-2y=-6

Answer 1

Answer:

x= -3 and y= 0

Step-by-step explanation:

5x+2y=-15

2x-2y=-6    

7x        =-21

x= -3

Putting value of x in equation 1  

5(-3) +2y=-15

-15+2y= -15

2y= 0

y= 0

This can be solved with the help of matrices

In matrix form the above equations can be written in the form

$\left[\begin{array}{ccc}5&2\\2&-2\/\end{array}\right]$  $\left[\begin{array}{ccc}x\\y\\\end{array}\right]$  = $\left[\begin{array}{ccc}-15\\-6\\\end{array}\right]$

Let

$\left[\begin{array}{ccc}5&2\\2&-2\/\end{array}\right]$ = A  $\left[\begin{array}{ccc}x\\y\\\end{array}\right]$  = X  and  $\left[\begin{array}{ccc}-15\\-6\\\end{array}\right]$= B

Then AX= B

or X= A⁻¹ B

where  A⁻¹= adj A/ ║A║   where mod A≠ 0

adj A=  $\left[\begin{array}{ccc}-2&-2\\-2&5\/\end{array}\right]$

║A║= ( 5*-2- 2*2)= -10-4= -14≠0

X= A⁻¹ B

 $\left[\begin{array}{ccc}x\\y\\\end{array}\right]$    =- 1/14  $\left[\begin{array}{ccc}-2&-2\\-2&5\/\end{array}\right]$   $\left[\begin{array}{ccc}-15\\-6\\\end{array}\right]$

 $\left[\begin{array}{ccc}x\\y\\\end{array}\right]$    =- 1/14     $\left[\begin{array}{ccc}-2*-15&+ -2*-6\\-2*-15&+ 5*-6\\\end{array}\right]$

 $\left[\begin{array}{ccc}x\\y\\\end{array}\right]$  =- 1/14 $\left[\begin{array}{ccc} 30&+12\\30&+-30\\\end{array}\right]$

 $\left[\begin{array}{ccc}x\\y\\\end{array}\right]$  =- 1/14 $\left[\begin{array}{ccc}42\\0\\\end{array}\right]$

$\left[\begin{array}{ccc}x\\y\\\end{array}\right]$  = $\left[\begin{array}{ccc}-42/14\\0/-14\\\end{array}\right]$

$\left[\begin{array}{ccc}x\\y\\\end{array}\right]$  = $\left[\begin{array}{ccc}-3\\0\\\end{array}\right]$

From here x= -3 and y= 0

Solution Set = [(-3,0)]