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daser333 [38]
3 years ago
7

I don’t really understand this type of stuff so please help.

Mathematics
1 answer:
ohaa [14]3 years ago
5 0

For 1 and 2, you plot both lines, and wherever they intersect is the solution to the system. Given the equation of a line, I think the easiest way to plot it is to find two points on the line, then draw a line through them. For example, if y=5x-1, then when x=0, you get y=-1; when x=1, you get y=4. So plot the points (0, -1) and (1, 4), then strike a line through.

1. Notice that dividing both sides of 2y=10x-2 by 2 returns y=5x-1, same as the first equation. So the system of equations reduces to one equation, which can have an infinite number of solutions. (This is because for any choice of x or y, you can always find a corresponding value for the other variable.)

2. See attached image. 3x-y=2 is given by the purple line.

For 3-6, you have several options. The two simplest methods of solving them are by substitution or elimination.

3. Like with (1), notice that dividing both sides of the first equation by 2 gives x+3y=9, so there will be an infinite number of solutions.

4. (by substitution) Since y=-7x+3, we can replace y in the second equation:

-7x+3+7x=10\implies3=10

but this is false, so there are no solutions to this system.

5. (by substitution) Since x=2y+2, in the first equation we have

-5(2y+2)+3y=-10y-10+3y=-7y-10=11\implies-7y=21\implies y=-3

Then back in the second equation we find

x=2(-3)+2=-6+2=-4

So (-4, -3) is the only solution here.

6. (by substitution) Notice that the left hand sides of both equations are the same, so we end up with 7 = 12, but this is false, so no solution exists.

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