Given System of Equations
5x-2y = 12
-5x+6y = -56
Add the equations straight down
The x terms cancel out (since 5x+(-5x) = 0x = 0)
The y terms combine to 4y
The right hand sides combine to -44
Therefore,
4y = -44
y = -44/4
y = -11
Use this to find x.
Pick either equation to plug in y = -11
I'll select the first equation
5x-2y = 12
5x-2(-11) = 12
5x+22 = 12
5x = 12-22
5x = -10
x = -10/5
x = -2
We have x = -2 and y = -11 pairing up together to get us the ordered pair solution (x,y) = (-2,-11)
We can confirm this through a graph
Here's the link to the interactive page
https://www.desmos.com/calculator/doa1oqrje8
Desmos is a free graphing app that I use often.
GeoGebra is another free graphing app I use all the time as well.
Notes:
5x-2y = 12 goes through the points (0,-6) and (2,-1)
-5x+6y = -56 goes through the points (4,-6) and (10,-1)
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A non-visual way to check the answer:
Plug (x,y) = (-2,-11) into the first equation
5x-2y = 12
5(-2)-2(-11) = 12
-10+22 = 12
12 = 12
We get a true statement.
Do the same for the second equation
-5x+6y = -56
-5(-2)+6(-11) = -56
10-66 = -56
-56 = -56
The second equation is confirmed as well.
Both equations are true when we plug in x = -2 and y = -11.
Therefore, the solution has been fully confirmed.
We can use WolframAlpha to help confirm the answer
In the search bar, type in 5x - 2y = 12 and -5x + 6y = -56
You could replace the "and" with a comma if you prefer.
This is what you should get
Here's the link
https://www.wolframalpha.com/input?i=5x+-+2y+%3D+12+and+-5x+%2B+6y+%3D+-56
WolframAlpha offers a graph, though it may be in a format you are unfamiliar with.
Notice the graphing window doesn't have the origin anywhere in view. This is because we're centered more around (-2,-11) which places us southwest of the origin. The good news is that the numbers along the side should help pinpoint where we are.
There are other software tools to quickly check the answer. With GeoGebra, you would type in Solve[{5x - 2y = 12,-5x + 6y = -56}]
The use of square brackets and curly braces are necessary. Feel free to explore your favorite software option to check the answer.
Though please don't rely on the software to replace your brain and do your homework for you. You'll still need practice when the exams happen.