Solve the system using any algebraic method. Please show work.?

Question

4x + 7y = -10
3x -7y = -4

Answer 1

ADD :-
7x = - 14
x = - 2

- 8 + 7y = - 10
7y = - 2
y = - 2 / 7

x = - 2 , y = - 2 / 7

Answer 2

There are two ways of doing this. One will work all the time but is sometimes more stenuous. The other will work some of the time and is very simple.

The simple version:

Start off with
4x + 7y = -10 you can add this equation to 3x -7y = -4

This yields

(4x+3x) +(7y-7y) = (-10 + -4)

wich equals

7x + 0 = -14

Dividing both sides by 7 we get:

x = -2

NOW YOU HAVE ONLY DONE HALF, you must substitute what you know back in to find what the value of y is.

so we take an easy equation and solve for y then put x in.

4x + 7y = -10 this solved for y is:

y = (-10 - 4x)/7

now putting x = -2 in where we have our x's

y = (-10 - 4*(-)2)/7
y = (-10 - (-8)) /7
y = (-2) / 7
y = -2/7

so x=-2 , y=(-2/7)

Now the method that will work all the time but is sometimes more difficult.
4x + 7y = -10
3x - 7y = -4

Solve one equation for one of the variables. Since we already solved for y we will use that one
y= (-10 -4x)/7

Now we substite that into the OTHER equation:
3x - 7((-10 -4x)/7)= -4

Simplifying
3x - (-10 -4x) = -4
3x + 10 + 4x = -4 ( we do this step by distributing the negative)
7x + 10 = -4
7x = -14
x = -14/7
x = -2

Now we have proved both ways that x = -2. Now you just follow the steps from when we substituted x = -2 above. This second way as you can see is a little tougher but will work all the time. Enjoy >:)

Answer 3

Add columns:

4x + 7y = -10
3x + -7y = -4
-----------------------
7x + 0y = -14

dividing both sides by 7 gives us x = -2

plug our x-value into original equation to solve for y:

4(-2) + 7y = -10

-8 + 7y = -10

add 8 to both sides:

7y = -2

divide by 7 to solve for y:

y = -2/7

so, our unknowns are solved to be:

x = -2, y= -2/7

note: either of original equations can be used to solve for y

Answer 4

4x+7y= -10
3x-7y= -4

since the y term (7y) can be easily cancelled, just add both equations.

(4x+3x) + (7y+(-7y)) = (-10+ (-4))

7x = -14
solve for x,
x= -2

using x= -2 in either equation,
3x - 7y = -4
3(-2) - 7y = -4
-7y = 2
y= -2/7

Answer 5

Add equations
7x=-14
x=-2
3x-7y=-4
3(-2)-7y=-4
-6-7y=-4
-7y=2
y=-2/7

Answer 6

add equation 1 and 2
we get 7x= --14
x= --2

put x=--2 in 1 eqn
-8+7y= -10
7y= -2
y= -2/7

check

substitute the value of x and y in eqn 2
-6 -7(-2/7) =-4
-6+2= -4
-4 = -4







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Answer 7

get x or y on one side by its self with no numbers, then plug it in for the x or y in the above equation..

like if you had... 3x+6y=12 and 2x+4y=8 you can take the 2nd equation and make it x=-2y+4 and plug that into the first one so you get
3(-2y+4)+6y=12 and solve for y, then plug y into one of your first to equations and solve for x..

Answer 8

x=(7y-4)/3

4(7y-4)/3 + 7=-10

28y/3-16/3+7/y=-10

49y/3=-14/3

y=-14/49=-2/7

3x-7y=-4

3x+2=-4

3x=-6

x=-2

Answer 9

This method is your best bet for solving systems of equations: [http://mathworld.wolfram.com/CramersRule.html] .
I can't emplain it any better...