Fill in the blank/s: When solving 3x^2 + 2y^2 = 35, 4x^2 + 3y^2 = 48 by the addition method, we can eliminate x2 by multiplying the first equation by -4 and the second equation by _________ and then adding the equations.

Question

Fill in the blank/s: When solving

3 x^{2} + 2 y^{2} = 35, 4 x^{2} + 3 y^{2} = 48

by the addition method, we can eliminate x2 by multiplying the first equation by -4 and the second equation by _________ and then adding the equations.

Answer 1

The equations given are

3 x^{2} + 2 y^{2} = 35, 4 x^{2} + 3 y^{2} = 48

.
We have to make the coefficients of

x^{2}

with same numbers but of opposite signs.
Here the lcm of coefficients of

x^{2}

in the first and second equations are lcm(3,4)=12. Thus, the we have to make the coefficients of x2 in the first and second equations as -12 and 12.
Thus, multiply the first equation by -4 and the second equation by 3 and then adding the equations.

Fill in the blank/s: When solving 3x^2 + 2y^2 = 35, 4x^2 + 3y^2 = 48 by the addition method, we can eliminate x2 by multiplying the first equation by -4 and the second equation by _________ and then adding the equations.

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