Question

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

Answer 1

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.