Question

Part 2 Directions: Solve the matrix equation for "X" and "y" 5 - 2x 6 1 -8 + 2 -8 4. - 13 -13​

Answer 1

Answer:

The value of x=9 and value of y= -7

Step-by-step explanation:

We need to solve the matrix equation for x and y

We are given:

$\left[\begin{array}{cc}-2x&6\\1&-8\\\end{array}\right] +2\left[\begin{array}{cc}5&-1\\y&6\\\end{array}\right] =\left[\begin{array}{cc}-8&4\\-13&-13\\\end{array}\right]$

First multiply 2 with terms inside the matrix

$\left[\begin{array}{cc}-2x&6\\1&-8\\\end{array}\right] +\left[\begin{array}{cc}10&-2\\2y&12\\\end{array}\right] =\left[\begin{array}{cc}-8&4\\-13&-13\\\end{array}\right]$

Now adding matrices on left side

$\left[\begin{array}{cc}-2x+10&6-2\\1+2y&-8+12\\\end{array}\right] =\left[\begin{array}{cc}-8&4\\-13&-13\\\end{array}\right]\\\left[\begin{array}{cc}-2x+10&4\\1+2y&4\\\end{array}\right] =\left[\begin{array}{cc}-8&4\\-13&-13\\\end{array}\right]$

Now both sides are equal , so we can say that

$-2x+10=-8 \ and \ 1+2y=-13$

Solving equations and finding values of x and y

Finding value of x

$-2x+10=-8 \\-2x=-8-10\\-2x=-18\\x=\frac{-18}{-2}\\x=9$

Finding value of y

$1+2y=-13\\2y=-13-1\\2y=-14\\y=\frac{-14}{2}\\y=-7$

So, value of x=9 and value of y= -7