Solve these pair of simultaneous equations
Y= 4x^2 - 5x + 2
Y= 2x -1
Thank you.
2x-1 = 4x^2-5x+2
4x^2 - 7x + 1 = 0
I get
4x^2 - 7x + 3 = 0
To solve this pair of simultaneous equations, we can use the method of substitution or elimination. Let's use the method of substitution:
Step 1: Solve one equation for one variable in terms of the other variable.
We have the second equation: Y = 2x - 1.
Let's solve this equation for x.
Step 2: Substitute the expression for the variable found in step 1 into the other equation and solve for the remaining variable.
We substitute 2x - 1 for Y in the first equation:
4x^2 - 5x + 2 = 2x - 1
Step 3: Simplify and solve the resulting equation.
Rearrange the equation by moving all terms to one side:
4x^2 - 5x - 2x + 1 - 2 = 0
Combine like terms:
4x^2 - 7x - 1 = 0
Now we have a quadratic equation. We can solve this equation using factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our quadratic equation: ax^2 + bx + c = 0,
a = 4, b = -7, and c = -1.
Substituting these values into the quadratic formula:
x = (-(-7) ± √((-7)^2 - 4(4)(-1))) / (2(4))
x = (7 ± √(49 + 16)) / 8
x = (7 ± √65) / 8
So we have two possible solutions for x.
Step 4: Substitute each value of x into one of the original equations to find the corresponding values of Y.
For the first value of x, x = (7 + √65) / 8:
Y = 2x - 1
Y = 2((7 + √65) / 8) - 1
Simplify and calculate Y.
For the second value of x, x = (7 - √65) / 8:
Y = 2x - 1
Y = 2((7 - √65) / 8) - 1
Simplify and calculate Y.
By following these steps, you will be able to find the solutions for the given pair of simultaneous equations.