Systems of equation help?

Question

How do i solve the following:

1. -2x-5y = 7
7x+y = -8

2. 4x+9y=2
2x+6y=1

thanks so much for the help

Answer 1

1.
-2x-5y = 7
7x+y = -8

We want to find x first. We will multiply the second equation by 5 and then we will add the two equalities:

7x + y = -8
is equivalent with this: (we multiply it by 5)
35x + 5y = -40
now we add this equation with
-2x-5x = 7
and the result is:
33x = -33
so
x = -1
We now replace x with -1 in 7x + y = -8
so
7(-1) + y = -8
-7 + y = -8
y = -1

so x = -1 and y =-1

2.
4x+9y=2
2x+6y=1

We want to find y first. We will multiply the second equation by -2 and then we will add the two equalities:

2x + 6y = 1
is equivalent with: (we multiply it by -2)
-4x - 12y = -2
we add this equality with
4x+9y=2
and the result is:
-3y = 0
so y = 0
we now replace y with 0 in this:
2x+6y=1
and we have:
2x=1
so:
x=1/2 and y =0

Answer 2

1. Solve the second equation for y to find y = -8 - 7x. Put this value of y into the first equation: -2x -5*(-8 - 7x) = 7 and solve for x. You will find x = -1. Now put this value for x into the previously found solution for y to get y = -8 - 7*(-1) = -1.

Now you should check this answer in the original equations.

Answer 3

I am doing the first one by substitution method and the second one by elimination method.
1)-2x-5y=7.....(eqn no 1)
7x+y= -8.....(eqn no 2)
From eqn no 2,we get
y= -8-7x
Pkugging y in eqn 1,we get
-2x-5(-8-7x)=7
=> -2x+40+35x=7
=> 33x=7-40= -33
x= -1
Plugging x in eqn 2 we get
y=-8+7= -1
Therefore x= -1 and y= -1 ans
2)4x+9y=2,,,,,(eqn 1)
2x+6y=1....(eqn 2)
Multiplying eqn 2 by 2 and subtracting it from eqn 1
4x+9y=2
4x+12y=2
(subtracting) -3y=0 or y=0
plugging y in eqn 1
4x+0=2
=>x=2/4=1/2
therefore,x=1/2 and y=0 ans

Answer 4

Q1) step1: for 7x+y=-8 set the equation so "y" can be by itself [tip: its easier to use this equation because "y" has no number in front]
7x+y=-8
-7x=-7x ---> y=-8-7x

step2: substitute "y=-8-7x into -2x-5y=7 so u can find the value of x!
-2x-5(-8-7x)=7
-2x+40+35x=7 <-----(combine like terms)
33x+40=7 <---(cancel out the 40 to get 33x by -------->-40=-40 itself)
33x=-33 <--(divide the "33" to get x by itself)
------------
33
x=-1!!!!

step3: now substitute x into "y=-8-7x" to get the value of y!
y=-8-7(-1)
y=-8+7
y=-1!!!!

step4: now substitute both values into "-2x-5y=7" and "7x+y=-8" to determine if both values are correct!
solution for -2x-5y=7:
-2(-1)-5(-1)=7
2+5=7
7=7

solution for 7x+y=-8
7(-1)+ -1=-8
-7 -1 =-8
-8=-8


do the same for Q2!
Q2)

Answer 5

1. -2x-5y = 7
7x+y = -8

y=-8-7x

-2x-5*(-8-7x)=7

find x and then find y