Solution of a system of equations
We want to find the value of x and y that satisfy both equations:
2x + 3y = 7
x + y = 3
We are going to solve it using the Elimination Method.
Elimination Method
We want to find an equation with only one variable based on both given equations.
We are going to add both sides of them.
In that addition we want that the term with x is 0.
In order to do it we transform the second equation multiplying it by -2, because
2x - 2x = 0x
Step 1: transforming the second equation
We multiply both sides of the second equation by -2:
x + y = 3
↓
-2(x + y) = -2 · 3
↓ since -2(x + y) = -2x - 2y and -2 · 3 = -6
-2x - 2y = -6
Then we have the equations:
2x + 3y = 7
x + y = 3
↓
2x + 3y = 7
-2x - 2y = -6
Step 2: adding both equations
Now we add each side of both equations:
2x + 3y = 7
-2x - 2y = -6
_________
0x + 1y = 1
Then, simplifying the result:
y = 1
Step 3: finding x value
We replace y by 1 on any of both original equations:
x + y = 3
↓ since y = 1
x + 1 = 3
↓ taking 1 to the right side
x = 3 - 1
x = 2
Step 4: ordered pair
In an ordered pair we wirte first the x value and then the y value:
(x, y)
↓
(2, 1)
Answer: B. (2, 1)