Is (7, -5) a solution to this system of equations? 2x – y = 19 4x + 3y = 13 a. yes b. no

To see if (7,-5) is a solution to the system of equations then you have to plug them in.

We can make life simpler by first simplifying the equations then plugging (7,-5) into the equations. You must plug them into both to completely make sure.

2x-y = 19 (solving for y)

1. Subtract 2x from both sides.

-y = 19-2x

2. Divide both sides by -1.

y = -19+2x

4x+3y = 13

1. Subtract 4x from both sides.

3y = 13-4x

2. Divide both sides by 3.

y = 13/3-4/3x

Now go ahead and plug them in to the newly simplified equations. Start with the first equation (y = -19+2x).

(7,-5) => -5 = -19+2(7)

-5 = -19+(14)

-5 = (-5), this is TRUE so that means so far (7,-5) is a possible solution. Moving on to the next equation (y = 13/3-4/3x).

(7,-5) => -5 = 13/3-4/3(7)

-5 = 13/3-28/3

-5 = -15/3

-5 = -5, this is also TRUE so that means that (7,-5) IS a solution to this system of equations.

Answer is:

A. Yes

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