Solve the system using elimination
2x-3y=-1
3x+4y=7
To solve this system using elimination, we need to eliminate one variable by adding or subtracting both equations.
We can start by multiplying the first equation by 4 and the second equation by 3 to make the coefficients of y the same:
4(2x - 3y) = 4(-1)
3(3x + 4y) = 3(7)
Simplifying these equations, we get:
8x - 12y = -4
9x + 12y = 21
Adding these two equations together, we eliminate the y variable:
(8x - 12y) + (9x + 12y) = -4 + 21
8x + 12y + 9x + 12y = 17
17x + 24y = 17
Dividing both sides of this equation by 17, we find the value of x:
x = 1
Substituting this value of x into the original first equation, we can solve for y:
2(1) - 3y = -1
2 - 3y = -1
-3y = -3
y = 1
Therefore, the solution to the system is x = 1 and y = 1.
To solve the system using elimination, we will eliminate one variable by adding or subtracting the equations.
First, let's eliminate the x variable. To do this, we can multiply the first equation by 3 and the second equation by 2:
(3) * (2x - 3y) = (3) * (-1)
(2) * (3x + 4y) = (2) * (7)
By simplifying, we get:
6x - 9y = -3
6x + 8y = 14
Now, let's subtract the equations:
(6x + 8y) - (6x - 9y) = 14 - (-3)
Simplifying, we get:
6x + 8y - 6x + 9y = 14 + 3
This simplifies to:
17y = 17
Next, we can solve for y by dividing both sides of the equation by 17:
17y/17 = 17/17
This gives us:
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
Simplifying, we get:
2x - 3 = -1
Adding 3 to both sides:
2x = 2
Dividing both sides by 2:
x = 1
So the solution to the system of equations is x = 1 and y = 1.
To solve the given system of equations using the elimination method, we will eliminate one of the variables by adding or subtracting the two equations together. Let's start by eliminating the variable "x" from the system.
Multiply the first equation by 3 and the second equation by 2 to make the coefficients of "x" in both equations the same:
Equation 1: 2x - 3y = -1
Multiply by 3: 6x - 9y = -3
Equation 2: 3x + 4y = 7
Multiply by 2: 6x + 8y = 14
Now, subtract the second equation from the first equation:
(6x - 9y) - (6x + 8y) = -3 - 14
This simplifies to:
-17y = -17
Divide both sides of the equation by -17:
y = 1
Now, substitute the value of y = 1 back into one of the original equations. Let's use Equation 1:
2x - 3(1) = -1
Simplify:
2x - 3 = -1
Add 3 to both sides of the equation:
2x = 2
Divide both sides of the equation by 2:
x = 1
Therefore, the solution to the given system of equations is x = 1 and y = 1.