How many solutions will the following system of linear equations have?

–2x + 4y = –7
y=-1/2x+5
A. 0
B. 1
C. 2
D. infinite

Question

How many solutions will the following system of linear equations have?

–2x + 4y = –7
y=-1/2x+5
A. 0
B. 1
C. 2
D. infinite

anonymous · Answer

As you should be able to determine by putting both equations in y=mx+b, then graph them, the lines then will intercept at exactly 1 point on the graph. This point will be the solution. There is 1 solution. Since they are linear. If, however you have non-linear systems, you may have more than 1 solution.

anonymous · Answer

Would you like me to show you how I arrived at this answer in more detail?

texaschic101 · Answer

its not necessary to graph...all you have to do is compare the slopes. Do you know how to do that Brandi ?

anonymous · Answer

No @texaschic101  Can you teach me?

texaschic101 · Answer

Cosmichaotic is correct in saying put the equations in y = mx + b form, where m is your slope. Once your equations are in this form, compare the slopes (the number in the m position) and the y intercepts (the number in the b position)

If the slopes and the y intercepts are the same, then the lines are coincident...they lie on top of each other, and therefore have infinite slopes.
If the slopes are the same, but the y intercepts are different, then the lines are parallel and have no solutions.
If the slopes and the y intercepts are different, then the lines only have 1 solution.

anonymous · Answer

Nicely explained @texaschic101

texaschic101 · Answer

y = -1/2x + 5
the number in the m position (the slope) is -1/2
the number in the b position (the y intercept) is 5

-2x + 4y = -7 (put this in y = mx + b form).....add 2x to both sides
4y = 2x - 7 -- divide both sides by 4
y = 2/4x - 7/4 -- reduce
y = 1/2x - 7/4
the number in the m position (the slope) is 1/2
the number in the b position (the y intercept) is -7/4

now compare the slopes and the y intercepts...
slopes and y intercepts are both different....this means there is only 1 solution

understand ?

anonymous · Answer

Yea i get. Thank you soooo much. So much easier now.

texaschic101 · Answer

no problem...you could solve it by graphing...but I only graph when I need to because I do not really like to graph...lol