Solve the system of equations using elimination.
−2x + 3y = 13
x + y = 11
First, we can simplify the system by multiplying the second equation by 2:
−2x + 3y = 13
2x + 2y = 22
Now we can add the two equations together, eliminating x:
5y = 35
Dividing both sides by 5, we get:
y = 7
Substituting this value back into the second equation, we can solve for x:
x + 7 = 11
x = 4
Therefore, the solution to the system is (4,7).
To solve the system of equations using elimination, we'll add the equations together to eliminate one variable.
First, let's multiply the second equation by 2 to create equal coefficients for x:
2(x + y) = 2(11)
2x + 2y = 22
Now we have the following system of equations:
-2x + 3y = 13
2x + 2y = 22
Adding the equations together eliminates the x variable:
(-2x + 3y) + (2x + 2y) = 13 + 22
-2x + 2x + 3y + 2y = 35
5y = 35
Now, we solve for y by dividing both sides of the equation by 5:
5y/5 = 35/5
y = 7
We substitute the value of y back into one of the original equations. Let's use the second equation:
x + y = 11
x + 7 = 11
Now, subtract 7 from both sides of the equation to solve for x:
x + 7 - 7 = 11 - 7
x = 4
So, the solution to the system of equations is x = 4 and y = 7.