Solving a system of equations by elimination involves adding or subtracting the equations to eliminate one of the variables, which allows you to solve for the other variable. Here's an example of how it works:
Let's say we have the following system of equations:
2x + 3y = 10 4x - y = 3
To solve this system of equations by elimination, we want to eliminate one of the variables, either x or y. In this case, we can eliminate y by multiplying the second equation by 3, so that the coefficient of y in both equations is the same, but with opposite signs:
2x + 3y = 10 12x - 3y = 9
Now we can add the two equations together to eliminate y:
14x = 19
To solve for x, we simply divide both sides by 14:
x = 19/14
Now we can plug this value of x into either of the original equations to solve for y. Let's use the first equation:
2x + 3y = 10
Substituting x = 19/14, we get:
2(19/14) + 3y = 10
Simplifying, we get:
3y = 37/7
To solve for y, we divide both sides by 3:
y = 37/21
So the solution to this system of equations is:
x = 19/14, y = 37/21
That's how you can solve a system of equations by elimination.