Wikipedia:Reference desk/Archives/Mathematics/2021 January 17

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January 17

Help with this question

I don't know how to solve this question. I am not asking you to do my homework, I just want to know how to solve a question like this.

y = 2x - 3

y = -x + 9

Help me solve. Koridas 📣 21:38, 17 January 2021 (UTC)

See System of linear equations#Elementary examples. -- Jack of Oz ^{[pleasantries]} 21:58, 17 January 2021 (UTC)

The section Elementary examples linked to above gives one method to solve a system of two linear equations with two unknowns, like in this case x and y. There are many other ways to do this. Suppose you have two equations

L₁ = R₁;

L₂ = R₂.

So, applied to the system above, L₁ stands for y and R₁ stands for 2x − 3. Then you can deduce that (to give just some examples) also each of the following equations holds:

L₁ = L₁;

R₁ = L₁;

L₁ + L₂ = R₁ + R2;

L₁ − L₂ = R₁ − R2;

2 L₂ = 2 R₂.

Also, if one left-hand side is the same as another right-hand side, as in

L₁ = R₁,

R₁ = R₂,

you can deduce that

L₁ = R₂,

L₁ = R₁

By playing a bit with such deductions, you will soon discover that you can easily obtain equations that are so simple that they are in fact the solutions for the unknowns. This is not a very systematic method, but if you regularly do this for such simple systems, you will quickly see what steps to take to get results. Once you have the solution, make sure to check that you haven't made a mistake by substituting the solutions in the original equations, to see if they turn into equalities, as they should.  --Lambiam 23:02, 17 January 2021 (UTC)

Hi, Koridas! Please see Equality (mathematics)#Basic properties. It says the relation is symmetric, which means if it holds for two values, then it holds in both directions. So if

y = 2x – 3

then also

2x – 3 = y

Another nice property is its transitivity. That one, based on

2x – 3 = y AND y = –x + 9

implies

2x – 3 = –x + 9

Can you continue from this? --CiaPan (talk) 23:07, 17 January 2021 (UTC)