What is the solution to this system of linear equations y-x=4 and y+2x=1
1 answer:
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Answer:
(x, y) = (5, -2)
Step-by-step explanation:
A graphing calculator provides a quick and easy way to find the solution.
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There are several other ways to solve these equations. Or you can estimate where the answer might be using logic like this:
The intercepts of the first equation are ...
- x-intercept = 26/4 = 6 1/2
- y-intercept = -26/3 = -8 2/3
So the graph of it will form a triangle with the axes in the 4th quadrant.
The intercepts of the second equation are ...
- x-intercept = 11/3 = 3 2/3
- y-intercept = 11/2 = 5 1/2
So the graph of it will form a triangle with the axes in the 1st quadrant. The x-intercept of this one is less than the x-intercept of the first equation, so the two lines must cross in the 4th quadrant.
The only 4th-quadrant answer choice is (5, -2).
The "m" in y = mx + b is the <u>slope.</u>
It is the number of units a point goes up, down, left, or right each time. Making the line linear/straight.
"rise" is the the number of units you go up(+) or down(-), "run" is the number of units you go to the right
For example, if your slope is:
You are going up 1 unit, and to the right 2 units
3 or
You are going up 3 units, and to the right 1 unit
You are going down one unit, and to the right 2 units
-3 or
You are going down 3 units, and to the right 1 unit