Question
How to find the value of x and y which satisfy both equations x-2y=24 and 8x-y=117
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Answer to a math question How to find the value of x and y which satisfy both equations x-2y=24 and 8x-y=117
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4.987 Answers
To find the values of x and y that satisfy both equations:
x - 2y = 24
8x - y = 117
You can use the method of substitution or elimination. Let's use the elimination method:
First, you can multiply the first equation by 8 to make the coefficients of y in both equations equal:
8(x - 2y) = 8(24) => 8x - 16y = 192
Now, you have the system of equations:
8x - 16y = 192
8x - y = 117
Next, subtract equation (2) from equation (1) to eliminate x:
(8x - 16y) - (8x - y) = 192 - 117
This simplifies to:
-15y = 75
Now, divide both sides by -15 to solve for y:
y = -75 / 15
y = -5
Now that you have found the value of y, you can substitute it back into one of the original equations to solve for x. Let's use equation (1):
x - 2(-5) = 24
x + 10 = 24
Subtract 10 from both sides:
x = 24 - 10
x = 14
So, the values that satisfy both equations are x = 14 and y = -5.
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