Question

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

Answer 1

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

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=(-18)/(-2)\\x=9`

Finding value of y

`1+2y=-13\\2y=-13-1\\2y=-14\\y=(-14)/(2)\\y=-7`

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