Answer: x = 4
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Work Shown:
Isolate y in the first equation
2x+y = 5
y = 5-2x .... subtract 2x from both sides
y = -2x+5
Then plug this into the other equation
-3x - 5y = 3
-3x - 5( y ) = 3
-3x - 5( -2x+5 ) = 3 .... replace y with -2x+5
-3x + 10x - 25 = 3 .... distribute
7x-25 = 3
7x = 3+25 .... adding 25 to both sides
7x = 28
x = 28/7 .... divide both sides by 7
x = 4 is the answer
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Optional Section:
Use this value of x to find y
y = -2x+5
y = -2(4)+5
y = -8+5
y = -3
Then we can check our answers by plugging them into the original equations
2x + y = 5
2(4) - 3 = 5
8 - 3 = 5
5 = 5
That confirms the first equation. Repeat for the second equation
-3x - 5y = 3
-3(4) - 5(-3) = 3
-12 + 15 = 3
3 = 3
We've confirmed both equations, so (x,y) = (4, -3) is the solution to this system. This system is considered independent and consistent.
Graphing the two original equations will show that they intersect at (4, -3).
