`2x - 3y  = -2, -4x + 9y = 7` Solve the system of linear equations and check any solutions algebraically.

Expert Answers

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You may use the reduction method to solve the system, hence, you may multiply the first equation by 2, such that:

`2(2x - 3y) = 2*(-2)`

`4x - 6y = -4`

You may now add the equation `4x - 6y = -4` to the equation -`4x + 9y = 7, ` such that:

`4x - 6y - 4x + 9y= -4 + 7`

`3y = 3 => y = 1`

You may replace 1 for y in equation `2x - 3y = -2` , such that:

`2x - 3 = -2 => 2x = -2 + 3 => 2x = 1 => x = 1/2`

Hence, evaluating the solution to the given system, yields `x = 1/2, y = 1.`

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