Answer:
(1,7)
[x = 1 and y = 7]
Explanation:
–10x − y = –17
5x − 2y = –9
Solving using elimination means that we'll use one equation to define one of the variables (x or y) and use that definition of x or y in the second equation. This has the effect of totally eliminating that variable that was defined, and we are left with an answer to the second variable. That value can then be used to find the first variable.
Lets use the first equation to define y [either x or y may be used, but this equation makes it easy to isolate y].
–10x − y = –17
-y = 10x - 17
y = -10x + 17
Now use this definition of y ion the second equation:
5x − 2y = –9
5x − 2(-10x + 17) = –9
5x + 20x -34 = -9
25x = 25
x = 1
Now use x = 1 in either equation to find y:
–10x − y = –17
–10(1) − y = –17 for x = 1
-10 - y = - 17
-y = -7
y = 7
Extra
Solving two linear equations means finding the point at which the two lines intersect. In other words, find a point, if any, that is a solution to both equations.
We can confirm this mathematically or graphically.
Math: Does the point (1,7) work for both equations?
–10x − y = –17
–10*1 − 7 = –17 for (1.7) ?
-17 = -17 YES
5x − 2y = –9
5*1 − 2*7 = –9 for (1,7) ?
5 - 14 = -9 ?
-9 = -9 YES
Graph: See the attached graph. YES