The system of equation 2x-y=o,x+3y=0 has
Answers
Answer:
Yes, you can solve the given system of two simultaneous equations by the substitution method as follows:
For the given system of two simultaneous linear equations in two variables x and y, we’ll arbitrarily choose the first equation and then solve for y in terms of x (we could have chosen to solve for x in terms of y):
2x + y = 0
2x + (‒2x) + y = 0 + (‒2x)
y = ‒2x
Now, substitute this expression for y into the other equation and then solve for x as follows:
x ‒ 3y = 0
x ‒ 3(‒2x) = 0
x + 6x = 0
7x = 0
(1/7)(7x) = (1/7)(0)
x = 0
Now, substituting this value for x into the equation y = ‒2x and solve for y as follows:
y = ‒2x
y = ‒2(0)
y = 0
Check (very important):
NOTE: In order for x = 0 and y = 0 to be the solution to the given system of simultaneous equations, they must satisfy (make true) both equations.
2x + y = 0 and x ‒ 3y = 0
2(0) + 0 = 0 0 ‒ 3(0) = 0
0 + 0 = 0 0 ‒ 0 = 0
0 = 0 0 = 0
Therefore, the solution set for the given system is {(0, 0)}.
Step-by-step explanation:
2x + y = 0
2x + (‒2x) + y = 0 + (‒2x)
y = ‒2x
Now, substitute this expression for y into the other equation and then solve for x as follows:
x ‒ 3y = 0
x ‒ 3(‒2x) = 0
x + 6x = 0
7x = 0
(1/7)(7x) = (1/7)(0)
x = 0
Now, substituting this value for x into the equation y = ‒2x and solve for y as follows:
y = ‒2x
y = ‒2(0)
y = 0
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