Solve the system of equations with the elimination technique. Please show your work.
3x + 2y = 1
2x - y = 3
To solve the system of equations using the elimination technique, we need to eliminate one of the variables. We can achieve this by multiplying the second equation by 2:
2(2x - y) = 2(3)
4x - 2y = 6
Now we have the two equations:
3x + 2y = 1
4x - 2y = 6
Adding these equations together, we eliminate the y variable:
(3x + 2y) + (4x - 2y) = 1 + 6
7x = 7
x = 7/7
x = 1
Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
3(1) + 2y = 1
3 + 2y = 1
2y = 1 - 3
2y = -2
y = -2/2
y = -1
So the solution to the system of equations is x = 1 and y = -1.
To solve the system of equations using the elimination technique, we'll start by multiplying the second equation by 2.
2(2x - y) = 2(3)
4x - 2y = 6
Now, our system of equations is:
3x + 2y = 1
4x - 2y = 6
Next, we'll add the two equations together to eliminate the variable y:
(3x + 2y) + (4x - 2y) = 1 + 6
3x + 4x + 2y - 2y = 7
7x = 7
Divide both sides of the equation by 7:
7x/7 = 7/7
x = 1
Now, substitute the value of x back into one of the original equations and solve for y. Let's use the first equation:
3(1) + 2y = 1
3 + 2y = 1
2y = 1 - 3
2y = -2
y = -1
A solution to the system of equations is x = 1 and y = -1.
To solve the system of equations using the elimination technique, we need to eliminate one of the variables by adding or subtracting the equations.
In this case, we will eliminate the variable "y". To do this, we need to multiply the second equation by 2 so that the coefficients of "y" in both equations will cancel each other out.
The original equations are:
1) 3x + 2y = 1
2) 2x - y = 3
Multiplying the second equation by 2, we get:
2 * (2x - y) = 2 * (3)
Which simplifies to:
4x - 2y = 6
Now, we have:
1) 3x + 2y = 1
3) 4x - 2y = 6
Next, add equations 1 and 3 to eliminate "y":
(3x + 2y) + (4x - 2y) = 1 + 6
3x + 4x = 7
Simplifying the left side of the equation gives us:
7x = 7
To solve for "x", divide both sides of the equation by 7:
7x/7 = 7/7
x = 1
Now that we have found the value of "x", we can substitute it back into one of the original equations to solve for "y". Let's use equation 1:
3x + 2y = 1
3(1) + 2y = 1
3 + 2y = 1
2y = 1 - 3
2y = -2
To solve for "y", divide both sides of the equation by 2:
2y/2 = -2/2
y = -1
Therefore, the solution to the system of equations is x = 1 and y = -1.
Use the elimination method to solve the follow system of equations.
9x−7y=22
x+3y=−24
This question requires you to show your work.
(1 point)
Responses
(0,−8)
open paren 0 comma negative 8 close paren
(4, 2)
(4, 2)
(−3,−7)