Solve the system using substitution.

2x + 5y =  -6

4x +  y = -12

Please explain how to solve this. Thank you 

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Solution:  x = -3, y = 0 or the ordered pair (-3, 0)

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Here's a system just like it solved that you can use as a model for

solving yours:

      6x + 7y = -42

      7x +  y =  -6

Pick an equation and a letter in it to solve for. If possible, to make things

easier, pick an equation that contains a letter which has an understood

coefficient 1 or -1, and solve that equation for that letter.

So in this problem we pick the second equation to solve for y, since it has

an understood coefficient of 1 in the second equation:

       7x + y = -6

            y = -6 - 7x

Next enclose the expression for y, namely -4-7x, in parentheses, and

replace y by it in the equation that you haven't used yet.

      6x + 7y = -42

6x + 7(-6-7x) = -42

6x - 42 - 49x = -42

    -43x - 42 = -42

         -43x = -42 + 42

         -43x = 0

            x = 0  

That's the value for x.  Now we must find the value for y.  Substitute 0 for

y in the equation solved for y above:

            y = -6 - 7x

            y = -6 - 7(0)

            y = -6 - 0

            y = -6

So the answer is x=0, y=-6 or the ordered pair (0, -6)

Edwin 

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