Use the system of equations to answer the question.
Information
Systems of Equations 1st row 2 x plus y equals 8 2nd row x minus 2 y equals negative 1
Question
What is the solution to the system of equations?
Answer options with 4 options
A.
the point negative 5, comma negative 2
B.
the point 2 comma 4
C.
the point 3 comma 2
D.
the point 5 comma 3
To find the solution to the system of equations, we can solve the equations using the method of substitution or elimination.
Let's solve the system using the method of elimination:
Equation 1: 2x + y = 8
Equation 2: x - 2y = -1
Multiply Equation 1 by 2 to make the coefficients of y in both equations equal:
Equation 1: 2(2x + y) = 2(8) -> 4x + 2y = 16
Now we can eliminate the y term by subtracting Equation 2 from Equation 1:
4x + 2y - (x - 2y) = 16 - (-1)
4x + 2y - x + 2y = 16 + 1
3x + 4y = 17 <-- New Equation 3
Now we have two equations:
Equation 3: 3x + 4y = 17
Equation 2: x - 2y = -1
Let's solve these two equations using the method of elimination again:
Multiply Equation 2 by 3 to make the coefficients of x in both equations equal:
Equation 2: 3(x - 2y) = 3(-1) -> 3x - 6y = -3
Now we can eliminate the x term by subtracting Equation 2 from Equation 3:
(3x + 4y) - (3x - 6y) = 17 - (-3)
3x + 4y - 3x + 6y = 17 + 3
10y = 20
y = 2
Now we can substitute the value of y into either Equation 1 or Equation 2. Let's use Equation 2:
x - 2(2) = -1
x - 4 = -1
x = -1 + 4
x = 3
Therefore, the solution to the system of equations is the point (3, 2).
The correct answer is therefore option C: the point 3,2.