ive got quite far but im stuck, can you go through each stage so i can check.
simultaneous equation with surds
5x-3y=41
(7root2)x+(4root2)y=82
thanks for the help
If you have gone far with the solution, what is bothering you?
If you post what you've got, we'll be glad to check instead.
tyet
3y =2x and x^2-y^2+2x-y=1
Sure! Let's go through the steps to solve the given simultaneous equations with surds.
Step 1: First, we need to get rid of the surds in the equations. To do this, we can multiply the first equation by 4√2 and the second equation by 7√2. This will help us to eliminate the surds when we add or subtract the equations.
Multiply the first equation by 4√2:
(4√2)(5x - 3y) = (4√2)(41)
20√2x - 12√2y = 164√2
Multiply the second equation by 7√2:
(7√2)((7√2)x + (4√2)y) = (7√2)(82)
98x + 56√2y = 574√2
Step 2: Now, we have two new equations:
20√2x - 12√2y = 164√2 ---(Equation 1)
98x + 56√2y = 574√2 ---(Equation 2)
Step 3: Next, we can add Equation 1 and Equation 2 together to eliminate the 'y' variable. When we add the two equations, the 'y' terms will cancel out:
(20√2x - 12√2y) + (98x + 56√2y) = (164√2) + (574√2)
20√2x + 98x - 12√2y + 56√2y = 738√2
Combining like terms:
118x + 44√2y = 738√2 ---(Equation 3)
Step 4: At this point, we have a simplified equation involving only 'x' and 'y'. Now, we can solve for one variable, let's say 'x', in terms of the other variable 'y' or vice versa. Let's solve for 'x' in terms of 'y' in Equation 3.
118x + 44√2y = 738√2
Subtract 44√2y from both sides:
118x = 738√2 - 44√2y
Divide both sides by 118:
x = (738√2 - 44√2y) / 118
Step 5: Now we have an expression for 'x' in terms of 'y'. We can substitute this expression for 'x' into one of the original equations to solve for 'y'.
Let's substitute x in the first equation:
5x - 3y = 41
5((738√2 - 44√2y) / 118) - 3y = 41
Simplify:
(369√2 - 22√2y) / 118 - 3y = 41
Step 6: At this stage, we have an equation involving only 'y'. We can now solve this equation to find the value of 'y'.
However, it seems that this equation may not have a simple surd solution. It is possible that the original problem was designed to have non-integer solutions. You may try simplifying further or using numeric methods like approximation or a calculator to find numerical solutions.
Please note that without any further simplification or other information, it is not possible to find an exact solution for 'y' in this case.