Question

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Solve the system using elimination.

2x−3y=−1
3x+4y=7

Answer 1

To solve the system using elimination, we need to eliminate one of the variables by adding or subtracting the equations.

To start, let's multiply the first equation by 3 and the second equation by 2 to make the coefficients of x in both equations the same:

(3)(2x - 3y) = (3)(-1)
(2)(3x + 4y) = (2)(7)

Simplifying these equations, we get:

6x - 9y = -3
6x + 8y = 14

Now we can subtract the first equation from the second equation to eliminate the x variables:

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

Simplifying this equation, we get:

6x - 6x + 8y + 9y = 14 + 3
17y = 17
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
2x - 3 = -1
2x = 2
x = 1

So the solution to the system of equations is x = 1 and y = 1.