I forgot how I can solve this Like this example:Solve for the

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In summary, to solve the system of equations modulo 7, you can combine the equations to eliminate one unknown and then solve for the remaining unknown. In this case, you can multiply the second equation by 3 and add it to the first equation to get a single equation in terms of x. Solving for x, you get x = 0. Substituting this back into the original equations, you can solve for y. Alternatively, you can solve the equations separately by substituting different values for x and y and checking if they satisfy both equations.
  • #1
XodoX
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I forgot how I can solve this... Like this example:

Solve for the integers modulo 7:

2x − 3y = 2
x + y = 4

Can somebody please explain this to me? Thanks!
 
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  • #2


Solve it just the way you would an ordinary system of equations- except work "modulo 7".
You want combine the equations to eliminate one unknown so you have a single equation in the other. Multiplying the second equation by 3 will give "-3y" in one equation and "+3y" in the second so adding will eliminate y.

2x- 3y= 2
3x+3y= 5 (3*4= 12= 7+ 5 so 12= 5 (mod 7))
Adding 5x= 0 (2+ 5= 7= 0 (mod 7) or you could have left the 12: 2+ 12= 14= 2(7)= 0 (mod 7). Of course, 5x= 0 gives us x= 0.

With x= 0, the two orignal equations are now -3y= 2 and y= 4. Which are compatible because -3(4)= -12= -14+ 2= 2(mod 7).
 
  • #3


Thanks. Can I not solve them separately,too?
 

FAQ: I forgot how I can solve this Like this example:Solve for the

How do I solve for a variable in an equation?

To solve for a variable in an equation, you must isolate the variable on one side of the equation by using inverse operations. This means that whatever operation is being done to the variable, you must do the opposite to cancel it out. For example, if you have the equation 2x + 5 = 15, you would subtract 5 from both sides to isolate the variable x.

What is the order of operations in solving equations?

The order of operations for solving equations is PEMDAS: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right). It is important to follow this order to correctly solve the equation.

Can I solve for a variable if there are fractions in the equation?

Yes, you can still solve for a variable if there are fractions in the equation. To do so, you must first get rid of the fractions by multiplying both sides of the equation by the least common denominator (LCD) of all the fractions in the equation. This will result in an equation without fractions that can be solved using inverse operations.

What do I do if there are variables on both sides of the equation?

If there are variables on both sides of the equation, you must first simplify the equation as much as possible by combining like terms. Then, you can isolate the variable on one side by using inverse operations. Finally, you can solve for the variable using the order of operations.

Is there a shortcut to solving equations?

There are some strategies and shortcuts that can be used to solve equations more efficiently. These include factoring, using the distributive property, and using algebraic rules such as the addition and multiplication properties of equality. However, it is important to remember that these shortcuts still follow the same principles of isolating the variable and using inverse operations to solve for it.

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