Answer:
5x-2x+7-x = 2x+8
5x-2x+7-x = 3x +8
5x-2x+7-x = 2x+7
Step-by-step explanation:
Now, the concept to understand here is, the definition of solution in a linear equation set.
These equations are representing lines, so when lines intersect at a point, the value of x coordinate and y coordinate on that point is solution set for these two lines.
Secondly, we need to understand the concept of slopes. Slope is the angle any line making with the x axis. Now, slope plays a really important part in solution sets of lines.
Consider a standard model of line
y = mx + b
now, m is the slope and b is the y-intercept. When any line intersect x and y coordinates the value of the y-coordinate at y axis and value of x coordinate on x axis at intersections is called x and y intercepts.
Now for equation given,
5x-2x+7-x
If you simplify it, it will become
2x + 7
Converting it into standard model
y = 2x + 7, you can see, m =2 and 7 =b.
So now for the question asked, if value of m is same for two lines, they will never intersect and there will be no solution for them.
That is why for question 1
5x-2x+7-x = 2x+8 is the answer because you can see that slope m for both equations is "2", hence there will be no solution.
For question 2
5x-2x+7-x = 3x +8, you can see that slope m for first equation is "2" while for second equation is "3", so they will intersect at one point and there will be one solution.
For question 3
5x-2x+7-x = 2x+7, you have to understand that in this case, the two lines are basically same and overlap each other, so they are not meeting at a single point, but both lines meet at every point on each other so there will be infinite solutions.
