solving simultaneous equations using elimination method?

Question

holiday maths homework but have no idea what to do.

3x + y = 2
4x + y =6

the book says: "Eliminate one variable by adding or subtracting the equations and hence solve the simultaneous equation".
what the hell is a variable!!

Answer 1

- 3x - y = - 2
4x + y = 6-----ADD
x = 4

12 + y = 2
y = - 10

x = 4 , y = - 10
Variables are x and y.

Answer 2

a variable represents a number through letters like x, y, z etc.

you just have to do this to get the unknown.

3x + y = 2
-1(4x + y = 6)-1

then it will become

3x + y = 2
-4x - y = -6

you can now eliminate y because one is negative and the other is positive. then add the remaining in the equation

-x = -4

multiply the equation by -1 then you'll get the value of x.

-1(-x = -4)-1
x = 4

to get the value of y, just substitute the value of x to the original equations and solve.

3x + y = 2
3(4) + y = 2
12 + y = 2
y = 2 - 12
y = -10

then the answer is x=4, y=-10.

if you want to make sure that the answer is correct, substitute the values to both equations. if the values satisfy the equation, then it's correct.

3x + y = 2 4x + y = 6
3(4) + (-10) = 2 4(4) + (-10) = 6
12 - 10 = 2 16 - 10 = 6
2 = 2 6 = 6

Answer 3

The variables in this and most other equations are x and y. The variable is what you are solving for, the unknown numbers in an equation. to solve this type of equation, I would multiply the bottom equation by -1. Then you add the 2 equations together to get -x=-4. Then you multiply by -1 again to get what x equals, 4.

You then substitute the known x variable (4) in for x in either equation. So in the top equation you would get 3X4+y=2. Multiply 3 by 4 and get 12. Subtract 12 from 2 to get -10 which is what y equals. So now you have solved for both x and y using the elimination method, you eliminate one variable and solved for the other.

Answer 4

The variables are x and y
from your question it is easier to get rid of y variable
simply by multiplying any equation by -1 to get
(let us multiply second one)
3x + y = 2
-4x + -y = -6
Now add two equations together
-x = -4 (but we want x value not -x) multiply with -1
x = 4
put the value of x for any equation
to get the value of variable y (let us put in first equation)
3(4) + y =2
12 + y =2
y = 2 - 12
y = 10
Therefor the values of variables are
x = 4
y = 10

Answer 5

There are a few ways. Here's one. Multiply the first equation by 4 which yields 4S+12L = 460. Then you can subtract the 2nd equation from it which with cancel the S variable. You can then solve for L, then substitute in the value of L to get the value of S. 4(S+3L=115) => 4S + 12L = 460 - 4S + L = 185 => 11L = 275 L = 25 Substitute L back in the get S. => 4S + 25 = 185 4S = 160 S = 40

Answer 6

x or y are the variables, if you have one negative variable and one positive when you add both equations they will eliminate each other. So if you multiply one equation by negative 1 and then add the equations you will end up with one single variable(y)
so
-1(3x+y=2)
= - 3x - y= -2
then add both equations:

-3x -y=-2

4x +y +6
________

x=4

then substitute the value of x in one equation and solve for y.

Answer 7

3x + y = 2
4x + y = 6

subtract the equations

the two "y"s cancel out and you are left with
-x = -4
x = 4

x and y are the two variables