The system of equations is given as:
x - 2y = 2
y = -2x + 5
To find the number of solutions, we can check if the lines represented by the equations intersect, are parallel, or coincide.
The first equation can be rearranged as x = 2y + 2.
Substituting this value for x in the second equation:
y = -2(2y + 2) + 5
y = -4y - 4 + 5
y = -4y + 1
Combining like terms, we get:
5y = 1
Solving for y, we get:
y = 1/5
Substituting this value for y in the first equation:
x - 2(1/5) = 2
x - 2/5 = 2
x = 2 + 2/5
x = 10/5 + 2/5
x = 12/5
Therefore, the system has one solution.
The correct option is: one solution.
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1 answer