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jeka94
3 years ago
10

Solve the simultaneous equation y-2x+1=0 and 4x^2+3y^2-2xy=7

Mathematics
1 answer:
Lapatulllka [165]3 years ago
8 0

The first equation is y-2x+1=0

y=2x-1 (Equation 1)

The second equation is 4x^{2}+3y^{2}-2xy=7 (Equation 2)

Putting the value of x from equation 1 in equation 2.

we get,

4x^{2}+3(2x-1)^{2}-2x(2x-1)=7

4x^{2}+3(4x^{2}+1-4x)-4x^{2}+2x=7

by simplifying the given equation,

12x^{2}-10x-4=0

6x^{2}-5x-2=0

Using discriminant formula,

D=b^{2}-4ac

D=25-4 \times 6 \times -2 = 73

Now the formula for solution 'x' of quadratic equation is given by:

x=\frac{-b+\sqrt{D}}{2a}  and  x=\frac{-b-\sqrt{D}}{2a}

x=\frac{5+\sqrt{73}}{12}  and x=\frac{5-\sqrt{73}}{12}

Hence, these are the required solutions.

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