6
AssignmentMultiple Select

Rewriting Equations to Use Substitution

Question 6 • (AG Q3) Math 8: 25-26 (JTurner)

Which systems of equations have no solutions? (Check all that apply.)

Answer
A
x – y = 1, –3x + 3y = 3
B
2y = 3 – 4x, x + y = 0
C
12x + 2 = 4y – 10, 2x + y = –11
D
–3x – y = 5, 15x = 10 – 5y
E
x + y = 1, –4x + 2y = 7

Explanation

In A, multiplying x − y = 1 by −3 gives −3x + 3y = −3, but the other equation says −3x + 3y = 3. The same expression cannot equal both numbers, so A has no solution. In D, the first equation is equivalent to 3x + y = −5, while the second is equivalent to 3x + y = 2; these are also inconsistent, so D has no solution.

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