To find the number of solutions to a system of equations, we can use the method of elimination or substitution.
1) Method of Elimination:
Multiply the first equation by 2 to make the coefficient of y the same in both equations:
4x = 2y + 8
Now we have the system of equations:
4x = 2y + 8
-4x + 2y = 2
Adding the two equations together, we eliminate the x term:
(4x + -4x) + (2y + 2y) = 8 + 2
0 + 4y = 10
4y = 10
y = 10/4
y = 5/2
Substituting this value of y back into the first equation:
2x = (5/2) + 4
2x = 5/2 + 8/2
2x = 13/2
x = 13/4
Therefore, the solution to the system of equations is x = 13/4 and y = 5/2.
2) Method of Substitution:
From the first equation, we can isolate y:
y = 2x - 4
Substitute this expression for y into the second equation:
-4x + 2(2x - 4) = 2
Simplify and combine like terms:
-4x + 4x - 8 = 2
-8 = 2
This equation is not true, which means there is no solution for x and y that satisfies both equations.
Therefore, the system of equations is inconsistent and has no solution.
Identify the number of solutions to the system of equation:
2x = y + 4
-4x + 2y = 2
1 answer