Let's solve the system of equations using elimination:
4x + 5y = 14
-4x -2y = -8
First, we need to get rid of one variable.
Sometimes we multiply them by some factors to have the same number on one variable, but in this case, we can subtract the x variable
4x +5y =14
-4x-2y = -8
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4x-4x =0, 5y -2y = 3y and 14-8=6
------------------------------
0+3y = 6
Solve the equation for y
Divide by 3 into both sides
3y/3 = 6/3
y = 2
Then, replace this variable on one equation, whichever you want:
4x + 5y = 14
4x +5(2) = 14
4x +10 = 14
and solve the equation for x
4x +10 = 14
Subtract 10 on both sides
4x +10-10 = 14-10
4x = 4
Divide by 4 into both sides
4x/4 = 4/4
x = 1
You can replace both variables to confirm the results:
4x +5y =14
4(1) +5(2) = 14
4 +10 = 14
14 = 14
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-4x -2y = -8
-4(1) -2(2) = -8
-4-4 = -8
-8 = -8
The result is correct, so my ordered pair is (x,y) = (1,2)