X-2y=-1
2x+y=4
solve each system using elimination. Tell whether the system has one solution, many solutions, or no solution.
2x+y = 4
Multiply first equation by 2.
2x - 4y = -2
Subtract first equation from second.
5y = 6
y = 6/5 = 1.2
To solve the system of equations using elimination, we'll eliminate one variable by adding or subtracting the two equations. Let's proceed step by step:
1. Multiply the second equation by 2 to make the coefficients of 'y' the same.
2(2x + y) = 2(4)
4x + 2y = 8
Now, we have the following system of equations:
X - 2y = -1
4x + 2y = 8
2. Add the two equations together:
(X - 2y) + (4x + 2y) = (-1) + 8
X + 4x = 7x = 7
Now, we have the equation:
7x = 7
3. Divide both sides of the equation by 7 to isolate 'x':
7x/7 = 7/7
x = 1
4. Substitute the value of 'x' into one of the original equations to find 'y'. Let's use the first equation:
X - 2y = -1
1 - 2y = -1
5. Solve for 'y':
-2y = -1 - 1
-2y = -2
y = (-2)/(-2)
y = 1
Therefore, the solution to the system of equations is x = 1 and y = 1.
To determine if the system has one solution, many solutions, or no solutions, we can observe that the variables 'x' and 'y' have unique values. Thus, the system has one solution.