1.

{{:(6x+3y=18),(qx -y/3=-2):} In the system of linear equations above, q is a constant. If the system has infinitely many solutions, what is the value of q?

Answer»

`-9`
`-2.3`
`2.3`
9

Solution :A SYSTEM of equations that has infinitely many solutions DESCRIBES a single line. Therefore, MANIPULATION of one equation will yield the other. Look at the constant terms: to turn the 18 into `1-2,` DIVIDED the first equation by `-9:`
`((6x+3y=18))/(-9)to - 6/9x - 3/9y=-2`
`to -2/3x -1/3 y =-2`
The y terms and constants in the second equation now match those in the first, all that's left is to SET the coefficients of x equal to each other : `q =-2/3.` Choice (B) is correct.
Note that you could also write each equation in slopeintercept form and set the slopes equal to each other to solve for q.


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