how do you solve -x+2y=2
what variable are you solving for?
If your solving for Y your answer is y=x/2 +1
If your solving for X your answer is x=2y-2
To solve the equation -x + 2y = 2, you can use the method of substitution or elimination.
Method 1: Substitution
1. Solve one of the equations for one variable in terms of the other variable.
In this case, let's solve -x + 2y = 2 for x:
x = 2y - 2
2. Substitute the expression obtained in step 1 into the other equation.
Replace x with 2y - 2 in the equation -x + 2y = 2:
-(2y - 2) + 2y = 2
3. Simplify and solve for the remaining variable.
Distribute the negative sign:
-2y + 2 + 2y = 2
2y - 2y = 2 - 2
0y = 0
Since 0y = 0 is always true, it means that the equation has infinitely many solutions. In this case, the equation represents a straight line.
Method 2: Elimination
1. Multiply both sides of the equation by a constant(s) to eliminate one variable.
In this case, let's multiply the entire equation by 2 to eliminate x:
-2x + 4y = 4
2. Add or subtract the two equations to eliminate one variable.
Subtract the new equation obtained in step 1 from the original equation:
-x + 2y - (-2x + 4y) = 2 - 4
-x + 2y + 2x - 4y = -2
x - 2y = -2
3. Solve the resulting equation for one variable.
x - 2y = -2
x = 2y - 2
This equation has infinite solutions, similar to what we obtained in Method 1. It represents a straight line as well.
In conclusion, the equation -x + 2y = 2 has infinite solutions and represents a straight line.