X+1/2y=5.5
-1/8x+1/4y=.25
Using elimination
multiply 2nd eqn. by two
subtract from 1st eqn. (to eliminate y)
Multiply the 1st Eq by 2 and the 2nd by 16. Then add:
2x + y = 11
-2x + 4y = 4
Sum: 5y = 15,
Y = 3.
In Eq1, replace y with 3 and solve for x.
Thank u
To use elimination to solve the given system of equations:
Step 1: Multiply both sides of one or both equations by appropriate constants to make the coefficients of one of the variables in both equations additive inverses (i.e., equal in magnitude but opposite in sign). This will allow you to eliminate that variable by adding the equations together.
In this case, we can choose to eliminate "x" by making the coefficients of "x" in both equations additive inverses. To do this, we can multiply the first equation by 1/8 and the second equation by 2.
The equations become:
(1/8)(x) + (1/16)(y) = (5.5)(1/8)
(-1/8)(x) + (1/4)(y) = (0.25)(2)
Simplifying these equations, we get:
(1/8)x + (1/16)y = 11/16
(-1/8)x + (1/4)y = 1/2
Step 2: Add the two equations together to eliminate "x".
(1/8)x + (-1/8)x + (1/16)y + (1/4)y = 11/16 + 1/2
Simplifying this equation will give us:
(3/16)y = (11/16 + 1/2)
Step 3: Solve for "y" by isolating it on one side of the equation.
(3/16)y = (11/16 + 1/2)
Combining the fractions on the right side:
(3/16)y = (11 + 8)/16
(3/16)y = 19/16
Now, we can solve for "y" by multiplying both sides of the equation by the reciprocal of (3/16), which is (16/3).
y = (16/3) * (19/16)
Simplifying this expression:
y = 19/3
Step 4: Substitute the value of "y" back into one of the original equations to solve for "x".
Using the first equation:
x + (1/2)(19/3) = 5.5
To simplify, multiply both sides of the equation by 2/1 to get rid of the fraction:
(2/1)x + (2/1)(1/2)(19/3) = (2/1)(5.5)
Which simplifies to:
2x + 19/3 = 11
Next, subtract 19/3 from both sides:
2x = 11 - 19/3
To combine the fractions on the right side:
2x = (33 - 19)/3
2x = 14/3
Now, divide both sides of the equation by 2 to solve for "x":
x = (14/3) / 2
x = 7/3
So, the solution to the system of equations is x = 7/3 and y = 19/3.