Answer:
(x,y)= 82/5, -17/2
Step-by-step explanation:
Write as a system of equation
5x + 8y = 14
6 - 9 - 2y = 14
solve the equation for y
6 - 9 - 2y = 14
calculate the difference
-3 - 2y = 14
move constant to the right side and change its sign
-2y = 14 + 3
add the numbers
-2y = 17
divide both sides of the equation by -2
y = -17/2
5x + 8y = 14
y = -17/2
substitute the given value of y into the equation 5x + 8y = 14
5x + 8 x (-17/2) =14
solve the equation for x
multiplying a positive and a negative equals a negative
2x -8 x 17/2 = 14
5x - 4 x 17 = 14
multiply the numbers
5x - 68 = 14
move constant to the right side and change its sign
5x = 14 + 68
Add the numbers
5x = 82
divide both sides of the equation by 5
x = 82/5
the possible solution of the system is the ordered pair (x , y)
(x,y) = (82/5, -17/2)
check if the given ordered pair is the solution of the system of equations
5 x 82/5 + 8x (-17/2) = 6 - 9 - 2x (-17/2) = 14
simplify the expression
14 = 14 = 14
since all of the equalities are true, the ordered pair is the solution of the system
(x, y) = (82/5, -17/2
