Find the simultaneous equation x-2y=1,y^2-3xy+8=0
1 answer:
Answer:
(-2.2, -1.6), (3, 1)
Step-by-step explanation:
You don't have to go far to find the equations. They are right there in your problem statement. Perhaps you want to find the solutions to the equations.
Use the first equation to write an expression for x, then substitute that into the second equation:
x = 2y +1
y^2 -3(2y+1)(y) +8 = 0
-5y^2 -3y +8 = 0
-(5y +8)(y -1) = 0
y = -8/5 or y = 1
The corresponding values of x are ...
x = 2(-8/5)+1 = -11/5
x = 2(1) +1 = 3
The solutions are (x, y) = (-2.2, -1.6) and (3, 1).
You might be interested in
15. The vertex form of f(x) = x² + 8x - 10 is f(x) = (x + 4)² - 26
17. The standard form of g(x) = (x + 3)² - 4 is g(x) = x² + 6x + 5
Step-by-step explanation:
Any quadratic function has:
1. A vertex form form f(x) = a(x - h)² + k, where (h , k) are the
coordinates of its vertex point
2. A standard form g(x) = ax² + bx + c, where a , b , c are constant and
a is the coefficient of x², b is the coefficient of x and c is the
y-intercept
3. the x-coordinate of the vertex point h = and
k = f(h)
15.
∵ f(x) = x² + 8x - 10
∴ a = 1 and b = 8
∵ h =
∴ h =
∴ h = -4
∵ k = f(h)
∴ k = f(-4)
- Substitute x by -4 in f(x)
∴ k = (-4)² + 8(-4) - 10
∴ k = 16 - 32 - 10
∴ k = -26
∴ f(x) = (x - -4)² + (-26)
∴ f(x) = (x + 4)² - 26
The vertex form of f(x) = x² + 8x - 10 is f(x) = (x + 4)² - 26
17.
∵ g(x) = (x + 3)² - 4
- Lets solve the power 2 of the bracket:
(1st + 2nd)² = (1st)(1st) + 2(1st)(2nd) + (2nd)(2nd)
∵ (x + 3)² = (x)(x) + 2(x)(3) + (3)(3)
∴ (x + 3)² = x² + 6x + 9
∴ (x + 3)² - 4 = (x² + 6x + 9) - 4
∵ 9 - 4 = 5
∴ (x + 3)² - 4 = x² + 6x + 5
The standard form of g(x) = (x + 3)² - 4 is g(x) = x² + 6x + 5
Learn more:
You can learn more about the vertex form of quadratic function in brainly.com/question/9390381
#LearnwithBrainly
Given:
Find the method .
Sol:
2eq(1) + eq(2) then,
Then apply the elimination method.