- #1
Yordana
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Determine the real numbers x and y from the equations:
I would appreciate it if someone could show me the solution to the first sub point.. 
Solving Equations with x and y: A Guide
- MHB
- Thread starter Yordana
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- Solving equations
In summary, the equations are (3+2i)x - (1-2i)y = 1+6i and (3x-y) + (2x+2y)i = 1+6i. To solve for the real numbers x and y, the simultaneous equations 3x-y = 1 and 2x+2y = 6 must be solved.
- #2
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The idea is that the real and imaginary components are the same on both sides of the equations. So for the first part:Yordana said:Determine the real numbers x and y from the equations: View attachment 11876 I would appreciate it if someone could show me the solution to the first sub point..
(3 + 2i)x - (1 - 2i)y = 1 + 6i
(3x - y) + (2x + 2y)i = 1 + 6i
So now you have the simultaneous equations
3x - y = 1
2x + 2y = 6
-Dan
- #3
Yordana
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Thank you!topsquark said:
1. What are the basic steps for solving equations with x and y?
The basic steps for solving equations with x and y are:
1. Isolate the variable terms on one side of the equation.
2. Simplify both sides of the equation.
3. Use inverse operations to eliminate any constants or coefficients.
4. Solve for the variable.
5. Check your answer by plugging it back into the original equation.
2. How do I know which inverse operations to use?
To determine which inverse operations to use, you must first identify the operations that are being performed on the variable. For example, if the variable is being multiplied by a number, you would use division as the inverse operation. If the variable is being added to a number, you would use subtraction as the inverse operation.
3. Can I solve an equation with more than one variable?
Yes, you can solve an equation with more than one variable. However, you will need as many equations as there are variables in order to solve for each variable. This is known as a system of equations and can be solved using various methods such as substitution or elimination.
4. What do I do if the equation has fractions or decimals?
If the equation has fractions or decimals, you can eliminate them by multiplying both sides of the equation by the denominator of the fraction or by a power of 10 for decimals. This will help simplify the equation and make it easier to solve.
5. Are there any shortcuts for solving equations with x and y?
Yes, there are some shortcuts for solving equations with x and y. For example, if the equation is in the form of y = mx + b, you can easily find the x-intercept (where the line crosses the x-axis) by setting y to 0 and solving for x. You can also use the slope formula (m = (y2-y1)/(x2-x1)) to find the slope of a line given two points on the line.
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