Simultaneous equations
5x + 3y= 31
2x + y = 12

a. find for x
b. find for y

x=5

y=2

Step-by-step explanation:

5x + 3y= 31

-6x - 3y = -36  (multiple  by -3)

-x=-5

x=5

2(5)+y=12   or         25 + 3y= 31

10+y=12                  3y=6

y=2                          y=2

x = 5, y = 2

Step-by-step explanation:

I'll use substitution on this one, which makes me choose one of the equation and solve for x. (5x + 3y = 31 was chosen)

5x + 3y = 31

Subtracct 3y from both sides

5x = -3y + 31

Divide both sides by 5

x = 1/5 (-3y + 31)

Multiply 1/5 by -3y + 31

x = -3/5y + 31/5

Substitute -3/5y + 31/5 for x in the other equation (2x + y = 12)

2 (-3/5y + 31/5) + y = 12

Multiply -3/5y + 31/5 by 2.

-6/5y + 62/5 + y = 12

Add -6/5y to y

-1/5y + 62/5 = 12

Subtract 62/5 from both sides

-1/5y = -2/5

Multiply both sides by -5

y = 2

Now head back to the previous equation, except substitute y for 2.

x = -3/5 * 2 + 31/5

Multiply -3/5 by 2.

x = (-6 + 31)/5

Add -6 and 31

x = 25/5

Divide 25 by 5.

x = 5

Formulate 5 and 2 for x and y in the equation.

5(5) + 3(2) = 31

2(5) + 2 = 12

25 + 6 = 31; true

10 + 2 = 12; true

x is 5 and y is 2.

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step-by-step explanatio89