Question 200483
Two positive numbers; x, y
;
Write an equation for each statement:
:
"the difference between two positive numbers is 4."
x - y = 4
-y = -x + 4
Multiply by -1;
y = (x - 4); use for substitution
:
"If twice the square of the larger number is added to three times the smaller, the sum is 53."
2x^2 + 3y = 53
:
Replace y with (x-4) in the above equation
2x^2 + 3(x-4) = 53
:
2x^2 + 3x - 12 - 53 = 0
Arrange as a quadratic equation:
2x^2 + 3x - 65 = 0
Factor
(2x + 13)(x - 5) = 0
Two solutions
2x = -13
x = -6.5,
and
x = +5; then y = 1; assume they want the integer solution
:
:
Check solution
2(5^2) + 3(1) = 53
:
:
The other solution: x=-6.5, y=-10.5, will also satisfy the equation
2(-6.5^2) + 3(-10.5) =
2(42.25) - 31.5 =
84.5 - 31.5 = 53