Answer:
Solution :
{x,y} = {2/3,2/3}
Step-by-step explanation:
Solve equation [2] for the variable x
[2] 9x = 6
[2] x = 2/3
// Plug this in for variable x in equation [1]
[1] (2/3) + 2y = 2
[1] 2y = 4/3
[1] 6y = 4
// Solve equation [1] for the variable y
[1] 6y = 4
[1] y = 2/3
// By now we know this much :
x = 2/3
y = 2/3
Answer: x = 4
y = -1
Step-by-step explanation:
Elimination Method:
In an elimination problem, both equations are aranged in the form of an arithmetic problem. One equation must have an offset of either the x or y of the other equation, so as to eliminate the variable for you to solve for the other one. If a variable doesn't have a negative counterpart, multiply the equation by a number so they can offset each other.
Given:
x + 2y = 2
-x + y = -5
Step 1: Solve for x
To solve for x, we need to eliminate the y by creating an equation where the y can eliminate the other equations y.
-2(-x + y = 5) = 2x - 2y = 10
Now that the y's can cancel each other out, we can combine the equations and solve for x.
x + 2y = 2
2x - 2y = 10
3x = 12
x = 12/3
x = 4
This is the value of x
Step 2: Solve for y
The x's can already cancel each other out, so you can just combine the equations and solve for y.
x + 2y = 2
-x + y = -5
3y = -3
y = -1
This is the value of y
Step 3: Verify
To make sure there weren't any mistakes, you need to check by replacing x and y with they're values. x is 4 and y is -1
Substitute: (4) + 2(-1) = 2
Solve: 4 - 2 = 2
Substitute: -(4) + (-1) = -5
Solve: -4 - 1 = -5
The answers are x = 4 and y = -1
