what is the solution of the following system of equations?
2y - x = 8
y = 2x + 1
a) (1,2)
b) (5,2)
c) (2,1)
d) (2,5)
and the answer i picked is c
thank you,
poo :)
Here is how to check your answer.
Plug your assumed values of x=2 and y=1 into the equations.
2y - x = 3, not 8
2x + 1 = 5, not 1
Your answer is therefore wrong. How did you get it?
Have you tried the method of substitution?
It tells you that
4x +2 -x = 8
3x = 6
You can take it from there.
To find the solution of the system of equations:
1) Start by rearranging the second equation to solve for y:
y = 2x + 1
2) Substitute the expression for y in the first equation:
2y - x = 8 becomes 2(2x + 1) - x = 8
3) Simplify the equation:
4x + 2 - x = 8
3x + 2 = 8
4) Subtract 2 from both sides:
3x = 6
5) Divide both sides by 3:
x = 6/3
x = 2
6) Substitute the value of x back into the second equation to find y:
y = 2x + 1 = 2(2) + 1 = 5
The solution to the system of equations is (2, 5), which does not match option c. So, the correct solution is not c, but the correct answer would be d) (2, 5).
To find the solution to the system of equations, you can use the method of substitution or the method of elimination. Let's solve it using the method of substitution:
Given equations:
1) 2y - x = 8
2) y = 2x + 1
Step 1: Substitute equation 2 into equation 1:
2(2x + 1) - x = 8
Step 2: Simplify equation 1:
4x + 2 - x = 8
3x + 2 = 8
Step 3: Subtract 2 from both sides:
3x = 6
Step 4: Divide both sides by 3:
x = 2
Step 5: Substitute the value of x into equation 2:
y = 2(2) + 1
y = 4 + 1
y = 5
So, the solution to the system of equations is (2, 5).
Since you chose option c) (2, 1), it appears to be incorrect. The correct answer is option d) (2, 5).
Please let me know if there's anything else I can help you with!