#### Question

# I Need Help With Algebra 1?

can anyone solve these?

Use linear combinations to solve the system of linear equations.

1. x+y=5

x-y=7

2. x-2y=8

-x+3y=-5

#### Answers

1)

Just combine the 2 equations.

x + x = 2x

y - y = 0

5 + 7 = 12

so...

2x = 12

x = 6

Now, substitute 6 for x in one of the equations:

6 + y = 5

Subtract 6 from both sides to isolate the y, so..

y = -1

2) Add the equations together just like the first one...

x - x = 0

-2y + 3y = y

8 - 5 = 3

so...

y = 3

Now, substitute the 3 for y in one of the equations...

x - 2(3) = 8

x - 6 = 8

Then, add 6 to both sides to isolate the x and you end up with...

x = 14

me too

1.) x = 6, y = -1

2.) x = 14, y = 3

1.) x=6

y=-1

2.) x=14

y=3

Single out the variable then use substitution.

x-y=7

x=7+y

7+y+y=5

2y=-2

y=-2/2=-1

now use -1 for y, x-1=5, x=6

x-2y=8

x=2y+8

-2y-8+3y=-5

y=3, plug that in for y

x-2(3)=8

x=14

I think this is Linear combination: I'm writing this out step by step

1. x+y=5 x-y=7

-y -y +y +y

_______ ________

x=5-y x=7+y

then combine the two equations

5-y=7+y

-y -y

________

5-2y=7

-5 -5

________

-2y=2

__ __

-2 -2

y=-1 Now plug -1 in for Y in the equation to get x, and try and figure out number two on your own