Question

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Which of the following is not a solution to the system of linear equations below?

A. (5, 6)
B. (–15, 12)
C. (0, 3)
D. (–10, –3)

Answer 1

To figure out which of the coordinates don't work, we need to substitute their values of x and y to figure out if they work or not. We will know they don't work if the result we get is something crazy like 2=25.

Substitute the values of x and y from a

`\left \{ {{5 (6) = 3(5) +15 } \atop {6(5)=10(6)-30}} \right.`

Now we simplify

`\left \{ {{30 = 30 } \atop {30=30} \right.`
Since this is true we know that the point (5,6) works. Now let's move onto B.

Once again, we substitute.

`\left \{ {{5 (12) = 3(-15) +15 } \atop {6(-15)=10(12)-30}} \right.`

This simplifies to

`\left \{ {{60=-30} \atop {-90=90} \right.`
Since this is obviously not right, we know that is the point that doesn't work in this system of equations.