Find the value of x and y in the simultaneous equation: 3x + y = 21; xy = 30
Question 1 Report
Find the value of x and y in the simultaneous equation: 3x + y = 21; xy = 30
Answer Details
To solve this system of equations, we can use substitution or elimination. Here's how to use substitution:
From the first equation, we can rearrange it to solve for y in terms of x:
3x + y = 21
y = 21 - 3x
Then we can substitute this expression for y into the second equation:
xy = 30
x(21 - 3x) = 30
Expanding the left side:
21x - 3x^2 = 30
Rearranging and factoring:
3x^2 - 21x + 30 = 0
Dividing by 3:
x^2 - 7x + 10 = 0
This quadratic equation can be factored as:
(x - 2)(x - 5) = 0
So the possible values of x are 2 and 5. To find the corresponding values of y, we can substitute each value of x into the expression we found for y:
When x = 2:
y = 21 - 3(2) = 15
When x = 5:
y = 21 - 3(5) = 6
Therefore, the solution to the system of equations is:
x = 2 or 5, y = 15 or 6
So the correct option is:
- x = 2 or 5, y = 15 or 6
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