How to solve this elimination
3x + y = 20
x + y = 12
To solve this system of equations using the elimination method, you need to eliminate one variable in order to solve for the other variable. Let's begin:
Step 1: Multiply the second equation by -1 to make the coefficient of y the same in both equations.
-1(x + y) = -1(12)
-x - y = -12
Now your system of equations becomes:
3x + y = 20
-x - y = -12
Step 2: Add the two equations together to eliminate the y variable.
(3x + y) + (-x - y) = 20 + (-12)
2x = 8
Step 3: Solve for x by dividing both sides of the equation by 2.
2x/2 = 8/2
x = 4
Step 4: Substitute the value of x back into one of the original equations. Let's use the first equation.
3(4) + y = 20
12 + y = 20
Step 5: Solve for y by isolating it on one side of the equation.
y = 20 - 12
y = 8
So the solution to the system of equations is x = 4 and y = 8.
Subtract the second equation from the first. This should give you
2x = 8
Divide both sides by 2 to get x, then substitute that value of x into either of your equations to get y.