Question 969467: which of the following system of linear equation has an infinite number of solutions? please show work.
a. 2x+5y=1, 6x+15y=3
b. x+y=10, x-y=4
c. x+y=10, x-y=16
d. x-2y=8, 2x+7y=-16
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! An infinite number of solutions means the same equation.
A is correct.
2x+5y=1 Multiply each term by 3, and you get 6x+15y=3, which is the other equation.
The second one has a solution at x=7 and y=3.
The third one has a solution at x=13 and y=-3
The 4th one has a solution at x=8 y=0.
What you look for are multiples. In A, I see 2x and 6x That is a multiple of 3. Then I look at y.
5y and 15 y, also multiple of 3. Then I look across the equals sign 1 and 3. This is the same equation.
Be careful, however. If the second were 6x=15y +3, this is not a multiple, because the x and y are on opposite sides of the equals sign.
x+y=something
x-y = something Almost always have a solution. Just add the x s and the y s disappear.
2x + 5y=1
6x+15y+3
Multiply top equation by 3 3{2x+5y=1) 3 * 2x=6x 3(5y)=15y 3*1=3 We distribute the 3 over every term in the equation
6x +15y=3
6x +15y=3 (the bottom equation)
Multiply the top equation by (-1). This changes all the signs.
-6x-15y=-3
6x +15y =3 Now add
0 + 0 = 0
This means that any x, y pair will work. Both of these equations describe the same line. I hope that helps!
I didn't show the solutions for the others, because the first one has an infinite number of solutions. It can be shown that the others do not.
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