Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Solve the system using elimination. 2x−3y=−1 3x+4y=7
To solve the system of equations using elimination, we will multiply both equations by a constant to make the coefficients of either x or y the same. Then we will add or subtract the equations to eliminate one variable and solve for the other.
First, let's multiply both sides of 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)
This simplifies to:
8x - 12y = -4
9x + 12y = 21
Now we will add the two equations to eliminate the y variable:
(8x - 12y) + (9x + 12y) = -4 + 21
This simplifies to:
17x = 17
Next, we will solve for x by dividing both sides of the equation by 17:
17x/17 = 17/17
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 substitute it into the first equation:
2x - 3y = -1
Replacing x with 1:
2(1) - 3y = -1
2 - 3y = -1
Next, we will isolate the y variable by subtracting 2 from both sides:
-3y = -1 - 2
-3y = -3
Finally, we solve for y by dividing both sides of the equation by -3:
y = -3 / -3
y = 1
Therefore, 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 need to eliminate one variable by adding or subtracting the equations.
Given system of equations:
2x - 3y = -1 ---(1)
3x + 4y = 7 ---(2)
We can eliminate the variable "x" by multiplying equation (1) by 3 and equation (2) by 2:
(3) 3(2x - 3y) = 3(-1) => 6x - 9y = -3
(4) 2(3x + 4y) = 2(7) => 6x + 8y = 14
Now, subtract equation (3) from equation (4):
(5) (6x + 8y) - (6x - 9y) = 14 - (-3)
6x + 8y - 6x + 9y = 14 + 3
17y = 17
Since the coefficient of y is 17, we can divide both sides of equation (5) by 17 to solve for y:
17y/17 = 17/17
y = 1
Now we substitute the value of y (=1) into one of the original equations. Let's substitute into equation (1):
2x - 3(1) = -1
2x - 3 = -1
2x = -1 + 3
2x = 2
x = 2/2
x = 1
Therefore, the solution to the given system of equations is:
x = 1
y = 1
To solve the system of equations using the elimination method, we need to eliminate one variable by manipulating the equations. Here are the steps:
Step 1: Multiply the first equation by 3 and the second equation by 2 to make the coefficients of "x" in both equations equal.
3 * (2x - 3y) = 3 * (-1)
2 * (3x + 4y) = 2 * 7
Simplifying the equations:
6x - 9y = -3
6x + 8y = 14
Step 2: Now we can subtract the first equation from the second equation to eliminate "x."
(6x + 8y) - (6x - 9y) = 14 - (-3)
6x - 6x + 8y + 9y = 14 + 3
17y = 17
Step 3: Divide both sides of the equation by 17 to solve for "y."
17y / 17 = 17 / 17
y = 1
Step 4: Substitute the value of "y" back into one of the original equations. Let's use the first equation:
2x - 3(1) = -1
2x - 3 = -1
Step 5: Solve for "x" by isolating the variable on one side of the equation.
2x = -1 + 3
2x = 2
x = 1
So, the solution to the system of equations is x = 1 and y = 1.