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Solve the system using elimination.
2x−3y=−1
3x+4y=7
To solve the system using elimination, we need to eliminate one of the variables by adding or subtracting the equations.
To start, let's multiply the first equation by 3 and the second equation by 2 to make the coefficients of x in both equations the same:
(3)(2x - 3y) = (3)(-1)
(2)(3x + 4y) = (2)(7)
Simplifying these equations, we get:
6x - 9y = -3
6x + 8y = 14
Now we can subtract the first equation from the second equation to eliminate the x variables:
(6x + 8y) - (6x - 9y) = 14 - (-3)
Simplifying this equation, we get:
6x - 6x + 8y + 9y = 14 + 3
17y = 17
y = 1
Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:
2x - 3(1) = -1
2x - 3 = -1
2x = 2
x = 1
So the solution to the system of equations is x = 1 and y = 1.
To solve the system using elimination, the goal is to eliminate one of the variables by adding or subtracting the equations.
Given the following system of equations:
2x - 3y = -1 ...(equation1)
3x + 4y = 7 ...(equation2)
Step 1: Multiply equation 1 by 3 and equation 2 by 2 to make the coefficients of x in both equations the same:
3 * (2x - 3y) = 3 * (-1)
2 * (3x + 4y) = 2 * 7.
This simplifies the system to:
6x - 9y = -3 ...(equation3)
6x + 8y = 14 ...(equation4)
Step 2: Now, subtract equation 3 from equation 4 to eliminate the variable x:
(6x + 8y) - (6x - 9y) = 14 - (-3)
6x + 8y - 6x + 9y = 14 + 3
17y = 17
y = 1
Step 3: Substitute the value of y = 1 into equation 1 or equation 2 to solve for x.
Using equation 1:
2x - 3(1) = -1
2x - 3 = -1
2x = -1 + 3
2x = 2
x = 2/2
x = 1
Therefore, the solution to the system of equations is x = 1 and y = 1
To solve the system using elimination, we need to eliminate one variable by multiplying one (or both) of the equations by a suitable constant so that the coefficients of one variable will become opposites of each other.
Let's start by eliminating the variable "x":
Step 1: Multiply the first equation by 3 and the second equation by 2 to create opposites for the coefficients of "x":
3(2x - 3y) = 3(-1)
2(3x + 4y) = 2(7)
Step 2: Simplify the equations:
6x - 9y = -3
6x + 8y = 14
Step 3: Subtract the first equation from the second equation:
(6x + 8y) - (6x - 9y) = 14 - (-3)
Simplifying further:
6x + 8y - 6x + 9y = 14 + 3
17y = 17
Step 4: Divide both sides of the equation by 17 to solve for "y":
17y/17 = 17/17
y = 1
Step 5: Substitute the value of "y" into one of the original equations to solve for "x". Let's use the first equation:
2x - 3(1) = -1
Simplifying further:
2x - 3 = -1
2x = 2
Step 6: Divide both sides of the equation by 2 to solve for "x":
2x/2 = 2/2
x = 1
Therefore, the solution to the system of equations is x = 1 and y = 1.