Write each system of linear equations as an augmented matrix:Part (a): 3x-y=-42x=y+2Part (b): x-3y-4z=-24x+2y+2z=52x-5y+7z=-8

Part (a): The augmented matrix is 3-1-42-12.Part (b): The augmented matrix is 1-3-4-242252-57-8.

Q. 198 - Intermediate Algebra

Write each system of linear equations as an augmented matrix:

Part (a): $\{\begin{cases} 3 x - y = - 4 \\ 2 x = y + 2 \end{cases}$

Part (b): $\{\begin{cases} x - 3 y - 4 z = - 2 \\ 4 x + 2 y + 2 z = 5 \\ 2 x - 5 y + 7 z = - 8 \end{cases}$

Verified

Answer

Part (a): The augmented matrix is $[\begin{array}{r} 3 & - 1 & - 4 \\ 2 & - 1 & 2 \end{array}]$ .

Part (b): The augmented matrix is $[\begin{array}{cccr} 1 & - 3 & - 4 & - 2 \\ 4 & 2 & 2 & 5 \\ 2 & - 5 & 7 & - 8 \end{array}]$ .

1Part (a) Step 1. Given information.

Consider the given system of equations,

$\{\begin{cases} 3 x - y = - 4 \\ 2 x = y + 2 \end{cases}$

Here, the second equation is not in standard form.

Rewrite the second equation in standard form,

$2 x = y + 2 2 x - y = 2$

2Part (a) Step 2. Write in augmented matrix.

Write the standard form of the second equation,

$\{\begin{cases} 3 x - y = - 4 \\ 2 x - y = 2 \end{cases}$

Write the augmented matrix,

$[\begin{array}{r} 3 & - 1 & - 4 \\ 2 & - 1 & 2 \end{array}]$

3Part (b) Step 1. Given information.

Consider the given system of equations,

$\{\begin{cases} x - 3 y - 4 z = - 2 \\ 4 x + 2 y + 2 z = 5 \\ 2 x - 5 y + 7 z = - 8 \end{cases}$

Here all the equations are in the standard form.

Write the augmented matrix,

$[\begin{array}{cccr} 1 & - 3 & - 4 & - 2 \\ 4 & 2 & 2 & 5 \\ 2 & - 5 & 7 & - 8 \end{array}]$