Which of the following are solutions to the system
{5x−2y=10−2.5x+y=−5? Select two answers.
A. (2,0)
B. (−2,−10)
C. (2,−5)
D. (−2,5)
E. (0, 2)
my first answer is c but im having trouble with finding the second answer :/
To find the solutions to the system of equations, we can use the method of substitution or elimination. Let's solve it using the substitution method.
We are given the following system of equations:
1) 5x - 2y = 10
2) -2.5x + y = -5
Let's solve equation 2) for y:
-2.5x + y = -5
y = 2.5x - 5
Now substitute the value of y in equation 1):
5x - 2(2.5x - 5) = 10
5x - 5x + 10 = 10
-5 + 10 = 0
From this, we can see that 0 does not satisfy the equation. Therefore, we need to consider other options.
Now, let's consider each of the given answer choices:
A. (2,0):
Substituting these values into the equations:
1) 5(2) - 2(0) = 10 (True)
2) -2.5(2) + 0 = -5 (True)
B. (-2, -10):
Substituting these values into the equations:
1) 5(-2) - 2(-10) = 10 (True)
2) -2.5(-2) + (-10) = -5 (True)
C. (2, -5):
Substituting these values into the equations:
1) 5(2) - 2(-5) = 10 (True)
2) -2.5(2) + (-5) = -5 (True)
D. (-2, 5):
Substituting these values into the equations:
1) 5(-2) - 2(5) = 10 (False)
2) -2.5(-2) + (5) = -5 (True)
E. (0, 2):
Substituting these values into the equations:
1) 5(0) - 2(2) = 10 (False)
2) -2.5(0) + (2) = -5 (False)
From the analysis above, we can see that answers A, B, and C are valid solutions to the system of equations. Thus, the correct answer is A. (2,0) and C. (2,-5).
The two equations are really the same line.
So, just pick any x (or y) and find the corresponding y (or x).
C is certainly wrong, since 5(2) - 2(-5) = 10+10 = 20 ≠ 10
A: y=0, so 5x=10 ==> x=2
Note that if y in(de)creases by 5, x in(de)creases by 2.
So, if x=0, y=-5
try decreasing x by another 2 and see what you get.