Question 1197249: Solve by using elimination method
8x+4y=16
4x-7y=26
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
4x-7y=26 is equivalent to 8x-14y=52 after multiplying both sides by 2.
We have this equivalent system of equations
8x+4y=16
8x-14y=52
Subtract the equations straight down.
8x-8x becomes 0
4y-(-14y) becomes 18y
16-52 becomes -36
We're left with 18y = -36 which solves to y = -2
I divided both sides by 18 to isolate y.
Use this y value to find x.
8x+4y=16
8x+4*(-2)=16
8x-8=16
8x=16+8
8x=24
x = 24/8
x = 3
Or,
4x-7y=26
4x-7(-2)=26
4x+14=26
4x=26-14
4x = 12
x = 12/4
x = 3
Or,
8x-14y=52
8x-14(-2)=52
8x+28=52
8x=52-28
8x=24
x = 24/8
x = 3
You only need to pick one equation involving x and y in it.
Solution: x = 3 and y = -2
This is equivalent to writing (x,y) = (3,-2)
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Check:
Plug those x and y values into the first original equation
8x+4y=16
8*3+4*(-2)=16
24-8=16
16=16
That verifies the first original equation.
Do the same for the second original equation
4x-7y = 26
4*3-7*(-2) = 26
12+14 = 26
26 = 26
Both equations are verified. The answer is fully confirmed.
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