Question

Match the system with its description. (To determine the description, first solve each system by the method you choose.) \frac{3}{1} \begin{cases} 4x - 3y = 5 \ -8x + 6y = -10 \end{cases} \frac{1}{1} \begin{cases} 5x - 2y = 20 \ 10x - 4y = -40 \end{cases} \frac{2}{1} \begin{cases} 2x - y = 4 \ x + 2y = 7 \end{cases} 1. Inconsistent system 2. Consistent, Dependent system 3. Consistent, Independent system

          Match the system with its description. (To determine the description, first solve each system by the method you choose.)
\frac{3}{1} \begin{cases} 4x - 3y = 5 \ -8x + 6y = -10 \end{cases}
\frac{1}{1} \begin{cases} 5x - 2y = 20 \ 10x - 4y = -40 \end{cases}
\frac{2}{1} \begin{cases} 2x - y = 4 \ x + 2y = 7 \end{cases}
1. Inconsistent system
2. Consistent, Dependent system
3. Consistent, Independent system

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Match the system with its description. (To determine the description, first solve each system by the method you choose.)
(3)/(1) 4x - 3y = 5 -8x + 6y = -10
(1)/(1) 5x - 2y = 20 10x - 4y = -40
(2)/(1) 2x - y = 4 x + 2y = 7
1. Inconsistent system
2. Consistent, Dependent system
3. Consistent, Independent system

Added by Robert H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Leslie Deeb

03/27/2022

Step 1

Step 2: Solve the second system of equations: 5x - 2y = 20 -10x - 4y = -40 Multiply the first equation by 2 to make the coefficients of x opposite: 10x - 4y = 40 -10x - 4y = -40 Add the two equations together: 0 = 0 Since 0 = 0, this system is consistent and Show more…

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Match the system with its description. (To determine the description, first solve each system using the method you choose.) 4x - 3y = 5 -8x + 6y = -10 5x - 2y = 20 -10x - 4y = -40 2x - y = 4 -2x - 2y = 7 1. Inconsistent system 2. Consistent, Dependent system 3. Consistent, Independent system

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Transcript

00:01 Okay, let's take a look at this system of three equations.

00:04 Now, i'll number them one, two, three, so you know which ones i'm talking about.

00:09 I'm going to start with two and three, and i like those two because i see that z and that negative z in two and three.

00:16 It's not the only choice for how to start this problem, it's just one option.

00:21 So here's those two equations as written.

00:24 I'm going to add them up, and when i do those zs, we'll cancel out.

00:28 So that's going to leave me with 7x plus y equals 0.

00:34 Now, i have to use equation 1.

00:38 So i can combine it with either of the other 2.

00:41 I'm just going to do 1 and 2.

00:43 So here they are, as written.

00:47 And again, i want those zs to cancel out.

00:50 So i'm going to multiply this bottom equation by 2.

00:54 So the top equation would stay the same.

00:57 The bottom equation would now be 6x minus 2y plus 2 z equals 0.

01:07 Let's add these two equations.

01:10 I get 7x minus y, z's cancel out, and it equals 0.

01:19 Now i have two equations, both in terms of x and y.

01:23 So let's deal with those two.

01:26 Again, i'm going to add them...

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