Answer:
Explanation:
y= 6+ 2x
8x - 4y = -20
a. My personal choice for how to solve this system of equations depends on how complex the equations are. Anything that is nonlinear, e.g., x^2 for example, I'll using graphing. For this particular system, I would go with either substitution or, if my computer is handy, go to the free DESMOS graphing site and find the intersection of the plotted lines. I don't know what "equal values" is, so I can't comment. Substitution and elimination are really the same thing, in my view.
I'll solve using both substitution and graphing:
Substitution:
y= 6+ 2x
8x - 4y = -20
We can use the first equation definition of y (6+2x) in the second equation:
8x - 4y = -20
8x - 4(6+2x) = -20
8x - 24 - 8x = -20
0x = 4
Well, that didn't work out well . . . .
Maybe I did something wrong. Let's try:
Graphing:
See the attached graph.
Zounds (metric term for "that's odd")
The lines appear parallel. If so, there is no solution - they never intersect. [They have a lot in common, too bad they'll never meet.]
Let's rewrite both equations in slope/intercept format of y = mx + b, where m is the slope and b is the y intercept (the value of y when x = 0)
---
y= 6+ 2x
y = 2x + 6
This line has a slope of 2, with an intercept of 6
8x - 4y = -20
-4y = -8x - 20
y = 2x + 5
This line also has a slope of 2, with an intercept of 5,
The lines are parallel so there is no solution. I should have rewritten both in slope-intercept form as a first step. One would spot the same slope and finished the problem: no solution. Using the DESMOS graphing tool was just as easy, and it helps build confidence in what is happening.