Solving Linear Systems- Substitution Method?

Question

I need to know how to do these three questions not just the answers.

D) 4x + y = -5

2x + 3y = 5

F) 3m -n = 5

5m -2n = 8

J) a + b

_ _ = 1

2 3

a + 2b

- - = -1

4 3

Answer 1

4x+y=-5

2x+3y=5

looking at the second equation, we can write

2x=5-3y

now, look at the first equation, which can be written as

4x=-5-y

but 4x = 2(2x)=-5-y

so we can substitute for 2x the expression 5-3y and get

2(5-3y)=-5-y

10-6y=-5-y

15=5y

y=3;

if y=3, sub this into the first equation to get:

4x+3=-5

4x=-8

x=-2

3m-n=5

5m-2n=8

the first equation can be written as n=3m-5, so subsitute this into the second equation and get:

5m-2(3m-5)=8

5m-6m+10=8

-m=-2

m=2;

substitute m=2 into the first equation:

3x2-n=5

6-n=5

n=1