Question

Choose the system of equations which matches the following graph.

5x − y = 7
2x − y = 0

5x − y = 7
2x + y = 0

5x + y = −7
2x + y = 0

5x + y = −7
2x − y = 0

Answer 1

@vishweshshrimali5

Answer 2

@mathmale

Answer 3

@reemii

Answer 4

Method 1: look at the graph and find a point (A) that lies on one line, and another point (B) that lies on the other line. (maybe the intersection.. that's just one point to look for).
Then, check each system: check if A verifies one equation and B the other.

Method 2: Determine the equation of the lines by looking at the graph, finding two points on each line and using the formula to write the equation of a line.

Method 3: rewrite all the equations in the form \(y = ax + b\) and this should give you some insight about which systems are impossible. The sign of the slope is a good place to look at. (FASTER but maybe not possible to conclude).

Answer 5

Let's start with the second equation of each system.
It's always "2x-y=0 " or "2x+y=0". If you isolate \(y\), you find either
\(y=2x\) or \(y=-2x\).
There is no "\(b\)" in these equations. That means lines with such equations must pass through the origin (0,0). Now look at the graph. How is the line which go through (0,0)? What is its slope?

Answer 6

I mean, "how": positive or negative?

Answer 7

negative?

Answer 8

yes. You can therefore eilminate the systems with \(2x-y=0\) as second equation (it is equivalent to \(y=2x\) which is the equation of a line with positive slope).

Answer 9

The remaining systems are the 2nd and the 3rd. Using a similar argument on the first equation, —and since the slope MUST be positive for this line— you eliminate system 3.
The answer is therefore System 2.


Actually, "Method 1" looks simpler. Because of the dashed lines, you can see that the point (1,-2) is the intersection of both lines. Therefore, all it takes to find the correct system is to check if (x=1,y=-2) is a solution of the system (verifies both equations).

Answer 10

Great!!! Once again thanks so much :)