Who is asking: Student
Level: Secondary

Question:
Hello, my name is john and while I was finishing up my work I stumbled into these problems.
a/4-b=-1
a+b=11
and
6a-b=-5
4a-3b=-8

Thanks a lot. I really need some help :)
John

Hi John,

There is more than one way to solve these sysyems of equations, but since the subject line of your email was "substitution method" let's use that method.

The first system is

 ^a/₄ - b = -1

a + b = 11

For the substitution method you want to use one of the equations to find an expression for one of the variables, either a or b. I am going to use the second equation to find an expression for b.

a + b = 11, so

b = 11 - a

Now that I have an expression for b I will substitute it into the other equation, in this case the first equation

^a/₄ - b = -1, so

^a/₄ - (11 - a) = -1

This equation has only one variable, a, so you can simplify and solve for a.

^a/₄ - (11 - a) = -1

^a/₄ - 11 + a = -1

 ^5a/₄ = 10

a = 8

If you substitute this value for a back into either of the original equations you can then solve for b. Make sure you check your answer when you are done.

For your second system of equations I would solve the first equation for b and then substitute into the second equation.

Cheers,
Penny

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