I feel so stupid but i forgot how to solve equations with 2 variables, how do you do it?

Question

how do you solve equations with 2 variables? for example

5b+7c= -22

how do you solve for b and c?

Answer 1

you must be given with another equation in the same 2 variables in order to answer this.

Answer 2

You can only solve for two variables when you have two (systems) or equations.

You can do this using the substitution method or the elimination method.

Example:  2x + y = 5      and     3x + 2y = 9

Substitution method

Solve the first equation for y:

2x + y = 5

-2x ....... -2x

y = 5 - 2x

Now substitute/replace y with y = 5 - 2x in the second equation and solve for x.

3x + 2(5 - 2x) = 9

3x + 10 - 4x = 9

3x - 4x + 10 = 9

- x + 10 = 9

-10 ....... -10

-x = -1 or x = 1

Now substitute x = 1 back into equation 1 to solve for y.

2x + y = 5

2(1) + y = 5

-2 ........  - 2

y = 3

Elimination method:

Multiply equation #2 by 2

3x + 2y = 9     ------------------------>    3x + 2y = 9

2(2x + y = 5)  ---------------------->  - 4x + 2y = 10

                                                          ____________

Subtract eq#2 from eq#1                - x         =  -1, or x = 1

2y - 2y ---> the y's cancel and you have solved for x.

Now substitute x = 1 into either equation to solve for y ...

3x + 2y = 9       ------------------> 2x + y = 5

3(1) + 2y = 9    ------------------>  2(1) + y = 5

3 + 2y = 9         ------------------->  2 + y = 5

-3 ....    -3          ------------------->    y = 3

2y = 6

y = 3

In this example, x = 1 and y = 3

Get it?

Answer 3

You need either some relationship between the two

variables or a second equation.

Then you can solve for one first and then get the second.