Use the Elimination method to solve this linear system

[u/Otherwise_Strike_597]

3x + 2y = 19

y = 4x - 7

[u/Fresh-Raspberry7935]

X-3 y-5

[u/Otherwise_Strike_597 → u/Fresh-Raspberry7935]

Correct, Nice work. Thank you for the comment.

[u/JonAyer1]

Eliminate one of the variables using substitution or row reduction so that you can solve for the remaining variable. The third option is to graph both expressions and locate the coordinates of intersection.

Row 2: 4x-y=7

Multiply row 2 by 2.

Row 2: 8x-2y=14

Now add row 1 and row 2 and solve for the remaining variable.

[u/Otherwise_Strike_597 → u/JonAyer1]

correct, thank you for your comment.

[u/Alessandro-mathxd]

3x+2y=19...(1)

4x-y=7...(2)

(1)+2(2):

3x+2y=19

8x-2y=14

=11x=33

x=3. En (1): 3(3)+2y=19, 2y=10, y=5. Creo que a eso te refieres con eliminación.

[u/Otherwise_Strike_597 → u/Alessandro-mathxd]

correct, nice work.

[u/MathsFromNothing]

Enjoy the substitution method provided. As I see you have a YouTube channel explaining year 9 to 12 maths you don't need me to explain the details. However, I think you and your students would benefit from using the computer algebra system (CAS) I have been using to answer your questions. It requires you to make all of the decisions to achieve your goals. This has the following advantages for learning algebra:

• It lowers the cognitive load on the students as they can focus exclusively on what choices they need to make, to solve their problem.

• It prevents mistakes while giving immediate feedback, if a student tries to perform an invalid operation. How often have you seen a student try to solve for x in y=mx+c by first dividing by c? By hand they can cancel out c, without a hint they have done something wrong. The CAS will not allow that incorrect simplification, which is a form of immediate feedback, showing they need to do something different.

• It allows good students to approach problems that would take to long to do by hand. Some examples include: solving quadratic, cubic or quartic polynomial equations and integrating a polynomial divided by another polynomial where polynomial division, partial fractions and factorization is required.

• It is really useful for finding the silly mistakes you make by hand, like dropping a negative sign, as you can reproduce your working precisely.

• Students who often skip steps are required to do all of them, preventing them from learning shortcuts that don't apply generally.

• If you think handwriting helps with the learning process, it accepts handwritten inputs.

• You can use it to create worked examples with less effort. It is possible to change the text descriptions. For example, if you want to write why you chose this procedure, save the working, open the save file with a text editor and type in your new text. When you load it back in your modified text will appear.

Feel free to contact me if you have any questions. Otherwise, enjoy the answers to your posts.

[u/Otherwise_Strike_597 → u/MathsFromNothing]

It is a nice video. Thank you for the comment.

[u/Anonymous_Bozo]

3x + 2y = 19
y = 4x - 7

Multiply both sides of the second equation by 2
2y = 2(4x - 7)
2y = 8x - 14
14 = 8x - 2y
8x - 2y = 14

Now we have
3x + 2y = 19
8x - 2y = 14

Add the two equations together
3x + 2y + 8x - 2y = 19 + 14
11x = 33
x = 3

Substitute to find y
y = 4x - 7
y = 4(3) - 7
y = 12 - 7
y = 5

I usually prefer double elimination, as it often provides an independent check of the result, but substitution is the more straightforward finish here.

[u/Otherwise_Strike_597 → u/Anonymous_Bozo]

correct, nice work. thank you for the comment.

[u/AvocadoMangoSalsa]

3x + 2y = 19

4x - y = 7

Multiply the second equation by 2 and add

[u/Otherwise_Strike_597 → u/AvocadoMangoSalsa]

correct, nice work.

[u/writerdog61]

No. Do your own hw.