solve 2x-y=11 and x+y=13 using the elimination method
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply one or both equations by a suitable constant to make the coefficient of either x or y the same.
Let's make the coefficient of y in both equations the same. To do this, we'll multiply the second equation by 2:
2(x + y) = 2 * 13
This gives us:
2x + 2y = 26
Now we have the system of equations:
2x - y = 11
2x + 2y = 26
Step 2: Add or subtract the equations to eliminate one of the variables.
Subtract the first equation from the second equation:
(2x + 2y) - (2x - y) = 26 - 11
This simplifies to:
2x + 2y - 2x + y = 15
Combine like terms:
3y = 15
Step 3: Solve for the remaining variable.
Divide both sides of the equation by 3:
3y/3 = 15/3
This gives us:
y = 5
Step 4: Substitute the value of y into one of the original equations to solve for the other variable.
We'll substitute y = 5 into the first equation:
2x - 5 = 11
Add 5 to both sides of the equation:
2x = 11 + 5
This simplifies to:
2x = 16
Step 5: Solve for x.
Divide both sides of the equation by 2:
2x/2 = 16/2
This gives us:
x = 8
So, the solution to the system of equations is x = 8 and y = 5.