Solve using the elimination method
3x+11y=34.5
9x-7y=-16.5
Eq1: 3X + 11Y = 34.5.
Eq2: 9X - 7Y = -16.5.
Multiply Eq1 by 9 and Eq2 by -3:
27X + 99Y = 310.5.
-27X + 21Y = 49.5.
Sum: 0 + 120Y = 360,
Y = 3.
In Eq1, substitute 3 for Y:
3X + 11*3 = 34.5,
3X = 34.5 - 33 =1.5,
X = 0.5.
Solution Set = (X,Y) = (0.5,3).
To solve these two equations using the elimination method, we need to eliminate one of the variables by multiplying one or both equations by a constant. Let's choose to eliminate the y variable.
First, let's multiply the first equation by 7 and the second equation by 11 to make the coefficients of y the same:
7 * (3x + 11y) = 7 * 34.5 -> 21x + 77y = 241.5 (Equation 1)
11 * (9x - 7y) = 11 * (-16.5) -> 99x - 77y = -181.5 (Equation 2)
Now, we can add the two equations together to eliminate the y term:
(Equation 1) + (Equation 2):
(21x + 77y) + (99x - 77y) = 241.5 - 181.5
Combining like terms, the y terms cancel out:
120x = 60
To solve for x, we divide both sides of the equation by 120:
x = 60 / 120
x = 0.5
Now that we have the value of x, we can substitute it back into either of the original equations to solve for y. Let's use the first equation:
3x + 11y = 34.5
Substituting x = 0.5:
3(0.5) + 11y = 34.5
Simplifying:
1.5 + 11y = 34.5
Subtracting 1.5 from both sides:
11y = 33
Dividing both sides by 11:
y = 3
Therefore, the solution to this system of equations is x = 0.5 and y = 3.