Which systems of equations have exactly one solution?

1 answer:

4 0

1.
$y=2x \\ y=2x+1 \\ \\
2x=2x+1 \\
2x-2x=1 \\
0=1 \\
not \ true - no \ solution$

2.
$x=5 \\
y=-4 \\
already \ solved - one \ solution$

3.
$y=x+6 \\
y-6=x \\ \\
y=x+6 \\
y=x+6 \\ \\
x+6=x+6 \\
x-x=6-6 \\
0=0 \\
true - infinitely \ many \ solutions$

4.
$y=3x+4 \\
y=3 \\ \\
3=3x+4 \\
3-4=3x \\
-1=3x \\
x=-\frac{1}{3} \\ \\
(x,y)=(-\frac{1}{3},3) - one \ solution$

The answer is 2 and 4.

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