2x − 5y = 16 3x + 2y = 5 Hi! Can you please help me with this? I've tried it but I just can't seem to figure it out! If you can, please provide an explanation. Thanks, have a good day!

x = 3, y = -2   →    (3, -2)

Step-by-step explanation:

Using Elimination Method, multiply the equations by a number that allows the coefficients of either x or y to be the same number with opposite signs. Then add the two equations to solve solve for the remaining variable.

I choose to eliminate x:

2x - 5y = 16    -->   3(2x - 5y = 16)   -->    6x - 5y  = 48

3x + 2y = 5    -->   -2(3x + 2y = 5)   -->   -6x - 4y = -10

                                                                     -19y = 38

                                                                    ÷19    ÷19

                                                                        y  =  -2

Next, substitute y = -2 into either equation to solve for x.

I choose the 1st equation:

2x -  5y  = 16

2x - 5(-2) = 16

2x +  10   = 16

2x            = 6

x             = 3

Check your answer by inputting x = 3 and y = -2 into the other (2nd) equation:

3x + 2y = 5

3(3) + 2(-2) = 5

9    +   -4    = 5

      5          = 5