solve the simultaneous equations for -2x+y=-3 and x+y=3
To solve the simultaneous equations -2x + y = -3 and x + y = 3, we can use the method of substitution or elimination.
Method 1: Substitution
Step 1: Solve one of the equations for one of the variables.
From the second equation, we can write y = 3 - x.
Step 2: Substitute the expression obtained in step 1 into the other equation and solve for the remaining variable.
Substitute y = 3 - x into the first equation:
-2x + (3 - x) = -3
-2x + 3 - x = -3
-3x + 3 = -3
-3x = -6
x = 2
Step 3: Substitute the value obtained in step 2 back into one of the original equations and solve for the other variable.
Using the second equation, y = 3 - x
y = 3 - 2
y = 1
Therefore, the solution to the simultaneous equations is x = 2 and y = 1.
Method 2: Elimination
Step 1: Add the two equations together to eliminate one of the variables.
-2x + y + x + y = -3 + 3
-y = 0
y = 0
Step 2: Substitute the value of y into either of the original equations and solve for the remaining variable.
Using the second equation:
x + y = 3
x + 0 = 3
x = 3
Therefore, the solution to the simultaneous equations -2x + y = -3 and x + y = 3 is x = 3 and y = 0.