Solve the system using elimination.
2x – 2y = –8
x + 2y = –1
And this one:
Solve the system using elimination.
3x – y = 28
3x + y = 14
Pleease help me :(
Of course! I'd be happy to help you solve these systems of equations using the elimination method. Let's start with the first one:
System 1:
2x - 2y = -8 ...(Equation 1)
x + 2y = -1 ...(Equation 2)
To eliminate one variable, we need to add or subtract the two equations. In this case, if we add Equation 1 and Equation 2 together, the y-term will cancel out.
Adding Equation 1 and Equation 2, we get:
(2x - 2y) + (x + 2y) = -8 + (-1)
3x = -9
Now, solve this equation for x by dividing both sides by 3:
(3x)/3 = -9/3
x = -3
Now substitute the value of x (-3) back into either Equation 1 or Equation 2. Let's use Equation 2:
x + 2y = -1
(-3) + 2y = -1
2y = -1 + 3
2y = 2
y = 1
So the solution to the first system of equations is x = -3 and y = 1.
Now, let's move on to the second system of equations:
System 2:
3x - y = 28 ...(Equation 1)
3x + y = 14 ...(Equation 2)
To eliminate the y-term, we will add the two equations together:
(3x - y) + (3x + y) = 28 + 14
6x = 42
Now, solve this equation for x by dividing both sides by 6:
(6x)/6 = 42/6
x = 7
Substitute the value of x (7) back into either Equation 1 or Equation 2. Again, let's use Equation 2:
3x + y = 14
3(7) + y = 14
21 + y = 14
y = 14 - 21
y = -7
Thus, the solution to the second system of equations is x = 7 and y = -7.
I hope this helps! Let me know if you have any further questions.
Of course! I'd be happy to help you solve these systems of equations using the elimination method.
Let's start with the first system of equations:
2x - 2y = -8 (Equation 1)
x + 2y = -1 (Equation 2)
The goal of the elimination method is to eliminate one variable by adding or subtracting the equations together. In this case, we can eliminate the "y" variable by adding Equation 1 to Equation 2.
Add Equation 1 and Equation 2 together:
(2x - 2y) + (x + 2y) = -8 + (-1)
Simplifying the equation:
2x - 2y + x + 2y = -8 - 1
Combine like terms:
3x + 0 = -9
We are left with the simplified equation:
3x = -9
To solve for "x", divide both sides of the equation by 3:
3x/3 = -9/3
Simplifying:
x = -3
Now that we have the value of "x", we can substitute it back into one of the original equations to solve for "y". Let's use Equation 2:
x + 2y = -1
Substitute x = -3:
-3 + 2y = -1
Simplifying:
2y = -1 + 3
2y = 2
To solve for "y", divide both sides of the equation by 2:
2y/2 = 2/2
Simplifying:
y = 1
So, the solution to the first system of equations is x = -3 and y = 1.
Now let's move on to the second system of equations:
3x - y = 28 (Equation 1)
3x + y = 14 (Equation 2)
Again, the goal is to eliminate one variable by adding or subtracting the equations together. In this case, we can eliminate the "y" variable by adding Equation 1 to Equation 2.
Add Equation 1 and Equation 2 together:
(3x - y) + (3x + y) = 28 + 14
Simplifying the equation:
3x - y + 3x + y = 42
Combine like terms:
6x + 0 = 42
We are left with the simplified equation:
6x = 42
To solve for "x", divide both sides of the equation by 6:
6x/6 = 42/6
Simplifying:
x = 7
Now that we have the value of "x", we can substitute it back into one of the original equations to solve for "y". Let's use Equation 2:
3x + y = 14
Substitute x = 7:
3(7) + y = 14
Simplifying:
21 + y = 14
To solve for "y", subtract 21 from both sides of the equation:
y = 14 - 21
y = -7
So, the solution to the second system of equations is x = 7 and y = -7.
I hope this explanation helps you understand how to solve systems of equations using the elimination method. Let me know if you have any further questions!
1st:
add them
3x = -9
x = -3
back into #2
-3 + 2y = -1
2y = 2
y = 1
2nd:
add them
6x = 42
x = 7
in the 2nd:
21 + y = 14
y = -7