Question

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

Answer 1

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.