# 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.

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.
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irwchh
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.