Algebra Help By 4 Today Please

[Leahbee5]

Without graphing, determine if the following system will have one solution, no solution, or an infinite number of solutions.

2x - y = 3

y = x + 4

[elliemay1]

x=7, y=11

[Prudie]

Rearrange the equations so they look the same:

2x-y = 3
x - y = -4

Now subtract the bottom one from the top one - this will make the ys disappera and leave:
x = 7 (3--4)

Substitute x + 7 into the firat to get
14 - y = 3
So y = 11

Check that works in the other equation
11 = 7 +4

So there is only 1 solution, x=7, y = 11

[elliemay1]

2x-(x+4)=3
2x-x-4=3
x=3+4=7
y=7+4=11

[Prudie]

and ignore my many typos, I was rushing!

[Old_Geezer]

No one minds helping someone understand how to do something, but your mass of maths question threads smacks of wanting someone to do your homework for you; to me.

[elliemay1]

Do you understand the methods used? Hope you have learnt something, leahbee.

[factor-fiction]

You don't even need to solve the simultaneous equations here.
You could simply rearrange these into:

y= 2x-3 and y= x+4

These are two straight lines with different gradients (2 and 1 respectively), so they can't be parallel. They must therefore meet and can only do so at one point. So there can only be one solution