Question

Given the system of equations, match the following items.

2 x - y = 0
x + y = -3

[0 -1
-3 1]

[2 0
1 -3]

[2 -1
1 1]

Answer 1

Explanation:

• x+y=-3

x = -3 -y

• 2x -y = 0

2(-3 -y) =0

-6 -2y = 0

-2y = 6

y = -3

• x = -3 -y

= -3 -(-3)

= -3+3 = 0

Answer 2

The x - determinant of the equation is
`\left[\begin{array}{cc}0&-1\\-3&1\\\end{array}\right]`

The y - determinant of the equation is
`\left[\begin{array}{cc}2&0\\1&-3\\\end{array}\right]`

The system determinant is
`\left[\begin{array}{cc}2&-1\\1&1\\\end{array}\right]`

How to find the determinants of x, y and the entire system?

The given system of equation include the following;

2x - y = 0

x + y = - 3

The x - determinant of the equation will be obtained by replacing coefficient of x with the constant terms.

`\Delta x = \left[\begin{array}{cc}0&-1\\-3&1\\\end{array}\right]`

The y - determinant of the equation will be obtained by replacing coefficient of y with the constant terms.

`\Delta y = \left[\begin{array}{cc}2&0\\1&-3\\\end{array}\right]`

The system determinant is obtained by removing the constant term and writing only the x and y coefficient in the matrix;

`\Delta = \left[\begin{array}{cc}2&-1\\1&1\\\end{array}\right]`