Which ordered pair represents the solution to:
System of equations 1st Row 2 x plus y equals 14 2nd Row 5 x minus y equals 28
Answer options with 5 options
A.
the point negative 6 comma negative 2
B.
the point 14-thirds comma negative 14-thirds
C.
the point 6 comma negative 2
D.
the point 6 comma 2
E.
the point negative 14-thirds comma 14-thirds
To solve this system of equations, we can use the method of substitution or elimination. Let's use the substitution method:
From the first equation, we have:
2x + y = 14
Solving for y, we can subtract 2x from both sides:
y = 14 - 2x
Now we can substitute this expression for y into the second equation:
5x - (14 - 2x) = 28
Expanding the equation and combining like terms:
5x - 14 + 2x = 28
7x - 14 = 28
Adding 14 to both sides:
7x = 42
Dividing both sides by 7:
x = 6
Substituting this value of x back into the first equation to solve for y:
2(6) + y = 14
12 + y = 14
Subtracting 12 from both sides:
y = 2
Therefore, the solution to the system of equations is the point (6, 2).
The correct answer option is D. The point 6 comma 2.
To find the solution to the system of equations, we can use either the substitution method or the elimination method.
Using the elimination method:
1st Row: 2x + y = 14
2nd Row: 5x - y = 28
Let's add the two equations together:
(2x + y) + (5x - y) = 14 + 28
2x + 5x = 42
7x = 42
x = 6
Now, substitute the value of x back into one of the equations to find y:
2(6) + y = 14
12 + y = 14
y = 14 - 12
y = 2
Therefore, the ordered pair that represents the solution to the system of equations is (6, 2).
The correct answer is D. the point 6, 2.
To find the solution to the system of equations, we need to solve the equations simultaneously. Let's start by rearranging the equations to solve for one variable in terms of the other.
First equation:
2x + y = 14
Rearranging the equation, we get:
y = 14 - 2x
Second equation:
5x - y = 28
Rearranging the equation, we get:
y = 5x - 28
Now that we have both equations in terms of y, we can set them equal to each other and solve for x.
Setting the two equations equal to each other:
14 - 2x = 5x - 28
Adding 2x to both sides:
14 = 7x - 28
Adding 28 to both sides:
42 = 7x
Dividing both sides by 7:
x = 6
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y.
Using the first equation:
2(6) + y = 14
12 + y = 14
Subtracting 12 from both sides:
y = 14 - 12
y = 2
Therefore, the ordered pair (x, y) that represents the solution to the system of equations is (6, 2). So the correct answer is D, the point 6 comma 2.