Simultaneous equation and surds
5x-3y=41
(7route2)x+(4route2)y=82
did you mean
7√2 x + 4√2 y = 82 ?
(that's "root" not "route")
how about multiplying the second equation by √2 ?
that would give you
14x + 8y = 82√2 or
7x + 4y = 41√2
I would then multiply the first equation by 4
and the last version of the second equation by 3,
then add them
take it from there.
i times them by 4 and 5 as you said and got
20x + 12y = 123
21x + 12y = 246�ã2
added together
21x = 123+246�ã2
is this right and if so can you help me get the next parts as i have tried but cant figure it out
thanks
To solve these simultaneous equations involving surds, we'll follow these steps:
Step 1: Isolate a variable in one of the equations
Step 2: Substitute the value of the isolated variable into the other equation
Step 3: Solve the resulting equation to find the value of the other variable
Step 4: Substitute the found value back into one of the original equations to solve for the remaining variable
Let's work through these steps:
Step 1: Isolate a variable in one of the equations
We'll isolate x in the first equation, "5x - 3y = 41".
Add 3y to both sides:
5x = 41 + 3y
Step 2: Substitute the value of the isolated variable into the other equation
The value of x in terms of y from the first equation is x = (41 + 3y) / 5.
Substitute this value into the second equation, "(7√2)x + (4√2)y = 82".
(7√2)((41 + 3y) / 5) + (4√2)y = 82
Step 3: Solve the resulting equation to find the value of the other variable
To get rid of the surds, we'll multiply everything by 5 to clear the fraction:
7√2(41 + 3y) + 4√2(5y) = 82(5)
Distribute and simplify:
287√2 + 21√2y + 20√2y = 410
Combine like terms:
(41√2)y = 410 - 287√2
(41√2)y = 410 - 287√2
Divide both sides by (41√2):
y = (410 - 287√2) / (41√2)
Step 4: Substitute the found value back into one of the original equations
We'll substitute the value of y we just found, y = (410 - 287√2) / (41√2), into the first equation:
5x - 3((410 - 287√2) / (41√2)) = 41
To simplify this equation, we'll multiply every term by (41√2) to clear the fraction:
5x * (41√2) - 3((410 - 287√2) / (41√2)) * (41√2) = 41 * (41√2)
Simplify and solve for x using algebraic manipulation.
Once you solve the equation for x, you'll have the values for both x and y, which would be the solution to the simultaneous equations.