Solve the following pair of simultaneous equations
X + y = 13
4x + y = 31

x = 6       y = 7

Step-by-step explanation:

You can isolate y using the first equation and get y = 13 - x.

Plug in for y using the second equation.

4x + (13 - x) = 31       Solve for x

4x - x = 18

3x = 18

x = 6                  Plug in for x using the first equation.

(6) + y = 13         Solve for y

y = 7

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The solution is (6, 7)

Step-by-step explanation:

Let's solve this system by elimination by addition and subtraction.  To accomplish this, subtract each term of the first equation by the corresponding term beneath it (e. g., subtract x in the first term from 4x in the second term):

3x = 18, which leads to x = 6.

Now substitute 6 for x in the first equation.  We get:  6 + y = 13, so y must be 7.

Substituting 7 for y in the second equation, we get 4x + 7 = 31, or 4x = 24.

Then x must be 6, and so

The solution is (6, 7)

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction