Write each system of linear equations as an augmented matrix:Part (a): 3x-y=-12y=2x+5Part (b): 4x+3y=-2x-2y-3z=72x-y+2z=-6

Part (a): The augmented matrix is 3-1-1-225.Part (b): The augmented matrix is 430-21-2-372-12-6.

Q. 196 - Intermediate Algebra

Write each system of linear equations as an augmented matrix:

Part (a): $\{\begin{cases} 3 x - y = - 1 \\ 2 y = 2 x + 5 \end{cases}$

Part (b): $\{\begin{cases} 4 x + 3 y = - 2 \\ x - 2 y - 3 z = 7 \\ 2 x - y + 2 z = - 6 \end{cases}$

Verified

Answer

Part (a): The augmented matrix is $[\begin{array}{r} 3 & - 1 & - 1 \\ - 2 & 2 & 5 \end{array}]$ .

Part (b): The augmented matrix is $[\begin{array}{cccr} 4 & 3 & 0 & - 2 \\ 1 & - 2 & - 3 & 7 \\ 2 & - 1 & 2 & - 6 \end{array}]$ .

1Part (a) Step 1. Given information.

Consider the given system of equations,

$\{\begin{cases} 3 x - y = - 1 \\ 2 y = 2 x + 5 \end{cases}$

Here, the second equation is not in standard form.

Rewrite the second equation in standard form,

$\begin{array}{rcl} 2 y & = & 2 x + 5 \\ - 2 x + 2 y & = & 5 \end{array}$

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

Write the standard form of the second equation,

$\{\begin{cases} 3 x - y = - 1 \\ - 2 x + 2 y = 5 \end{cases}$

Write the augmented matrix,

$[\begin{array}{r} 3 & - 1 & - 1 \\ - 2 & 2 & 5 \end{array}]$

3Part (b) Step 1. Given information.

Consider the given system of equations,

$\{\begin{cases} 4 x + 3 y = - 2 \\ x - 2 y - 3 z = 7 \\ 2 x - y + 2 z = - 6 \end{cases}$

Here all the equations are in the standard form.

Write the augmented matrix,

$[\begin{array}{cccr} 4 & 3 & 0 & - 2 \\ 1 & - 2 & - 3 & 7 \\ 2 & - 1 & 2 & - 6 \end{array}]$