Answer: (x,y) = (5,2)
In other words, x = 5 and y = 2
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Step-by-step explanation:
Subtract the equations straight down.
- The x terms subtract to 3x-3x = 0x and they go away (hence the term "elimination").
- The y terms subtract to 4y-(-2y) = 6y
- The right hand sides subtract to 23-11 = 12
We end up with 6y = 12 which solves to y = 2 after dividing both sides by 6.
Now use this y value to find x.
If we used the first equation, then we have these steps
3x+4y = 23
3x+4(2) = 23
3x+8 = 23
3x = 23-8
3x = 15
x = 15/3
x = 5
Or we could use the second equation
3x-2y = 11
3x-2(2) = 11
3x-4 = 11
3x = 11+4
3x = 15
x = 15/3
x = 5
We get the same x value either way.
The solution is (x,y) = (5,2)
To check the answer, plug those coordinates into each equation. After simplifying, you should get the same number on both sides.
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Check:
3x+4y = 23
3(5)+4(2) = 23
15+8 = 23
23 = 23 .. that works
and,
3x-2y = 11
3(5)-2(2) = 11
15 - 4 = 11
11 = 11 .. that works as well
Both original equations are true for those x and y values.
The solution is fully confirmed.