To eliminate x, on the addition of two equations, we multiply the first equation by -10, and the second equation by 3. Thus, option (A) –10 times the first equation and 3 times the second equation, is the right choice.
What is a system of equations?
A system of equations is a set of equations, involving similar variables used to solve for the variables simultaneously.
How to solve the question?
In the question, we are asked for the numbers which when multiplied by the two equations respectively, eliminate x, when the equations are added.
The two equations are:
(1/5)x + (3/4)y = 9 ... (i),
(2/3)x - (5/6)y = 8 ... (ii).
We know that to eliminate a variable from a system of equations, their coefficients need to be equal and the sign needs to be opposite.
In the question, we are asked to eliminate x.
The coefficients of x are (1/5) and (2/3).
To equalize the coefficients, we make them equal to their LCM.
LCM of (1/5) and (2/3) is 2.
To make (1/5) as 2, we need to multiply it by 10.
To make (2/3) as 2, we need to multiply it by 3.
For opposite signs, we will make of this negative.
The option with our calculations is A. –10 times the first equation and 3 times the second equation.
Thus, to eliminate x, on the addition of two equations, we multiply the first equation by -10, and the second equation by 3. Thus, option (A) –10 times the first equation and 3 times the second equation, is the right choice.
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