simultaneous equation: 4x-9y^2=19, 2x+3y=11
since 2x = 11-3y, 4x = 22-6y. So,
22-6y - 9y^2 = 19
9y^2 + 6y - 3 = 0
3(3y-1)(y+1) = 0
Now you know two values of y, and each will provide a value for x.
The line intersects the parabola at two points.
I want to achieve
love it
To solve the simultaneous equations:
1. First, let's rearrange the second equation to solve for x:
2x + 3y = 11
Subtract 3y from both sides:
2x = 11 - 3y
Divide by 2:
x = (11 - 3y) / 2
2. Now we can substitute this value of x into the first equation:
4x - 9y^2 = 19
Replace x with (11 - 3y)/2:
4((11 - 3y)/2) - 9y^2 = 19
3. Simplify the equation:
Distribute 4 into the parentheses:
(44 - 12y)/2 - 9y^2 = 19
Simplify the left side:
44/2 - 12y/2 - 9y^2 = 19
22 - 6y - 9y^2 = 19
Rearrange in descending order:
-9y^2 - 6y + 22 = 19
Subtract 19 from both sides:
-9y^2 - 6y + 22 - 19 = 0
-9y^2 - 6y + 3 = 0
4. Now we have a quadratic equation. To solve it, we can use the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = -9, b = -6, and c = 3. Plug these values into the quadratic formula and solve for y.
5. Once you find the values of y, substitute them back into the second equation (2x + 3y = 11) to solve for x.
By following these steps, you can find the values of x and y that satisfy both equations, if they exist.