If x = −2 and x2 + y2 + 3xy = −5, then find y
Question
If x = −2 and x2 + y2 + 3xy = −5, then find y
Solution 1
To find the value of y, we can substitute the given value of x into the equation x^2 + y^2 + 3xy = -5.
Step 1: Substitute x = -2 into the equation: (-2)^2 + y^2 + 3(-2)y = -5
Simplifying this equation, we get: 4 + y^2 - 6y = -5
Step 2: Rearrange the equation: y^2 - 6y + 4 + 5 = 0
Simplifying further, we have: y^2 - 6y + 9 = 0
Step 3: Factor the equation: (y - 3)^2 = 0
Step 4: Solve for y: y - 3 = 0 y = 3
Therefore, the value of y is 3.
Solution 2
To find the value of y, we can substitute the given value of x into the equation x^2 + y^2 + 3xy = -5.
Step 1: Substitute x = -2 into the equation: (-2)^2 + y^2 + 3(-2)y = -5
Simplifying this equation, we get: 4 + y^2 - 6y = -5
Step 2: Rearrange the equation: y^2 - 6y + 4 + 5 = 0
Simplifying further, we have: y^2 - 6y + 9 = 0
Step 3: Factor the equation: (y - 3)^2 = 0
Step 4: Solve for y: y - 3 = 0 y = 3
Therefore, the value of y is 3.
Similar Questions
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