Question

Solve the system using elimination. 2x−3y=−1 3x+4y=7

Answer 1

To solve the system using elimination, we can multiply the first equation by 3 and the second equation by 2 to create opposite coefficients for y.

First equation: 2x - 3y = -1
Second equation: 3x + 4y = 7

Multiply the first equation by 3:
3(2x - 3y) = 3(-1)
6x - 9y = -3

Multiply the second equation by 2:
2(3x + 4y) = 2(7)
6x + 8y = 14

Now, we can add the two new equations:

(6x - 9y) + (6x + 8y) = -3 + 14
12x - y = 11

So, the simplified system of equations is:
12x - y = 11
3x + 4y = 7

We can solve for x by multiplying the second equation by 3 and the first equation by 4 to create opposite coefficients for x:

Multiply the first equation by 4:
4(12x - y) = 4(11)
48x - 4y = 44

Multiply the second equation by 3:
3(3x + 4y) = 3(7)
9x + 12y = 21

Now, we can add the two new equations:

(48x - 4y) + (9x + 12y) = 44 + 21
57x + 8y = 65

So, the updated system of equations is:
57x + 8y = 65
9x + 12y = 21

We can now solve this system using elimination or another method.