1.

{{:(3x -9y=-6),(1/2x-3/2y=c):} If the system of linear equations above has infinitely many solutions, and c is a constant, what is the value of c ?

Answer»

`-6`
`-3`
`-2`
`-1`

Solution :A system of LINEAR equations has infinitely many solutions if both lines in the system have the same slope and the same y-intercept (in other words, they are the same line).
To have the same slope, the x-and y-coefficients of the two equations MUST be the same. Use the x-coefficients here: to turn `1/2` into 3, multiply by 6, So c becomes 6C, and `6c =- 6, or c =-1,` which is (D).
Note that you could ALSO write each equation in slopeintercept form and set the y-intercepts equal to each other to solve for c.


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