Identify the solution(s) of the system of equations, if any.
2x + 5y =10
Y = 2 – x
a) (-2,0)
b) (2,0)
c) (0,-2)
d) (0,2)
2 x + 5 (2-x) = 10
2 x - 5 x + 10 = 10
-3 x = 0
x = 0
y = 2-x = 2
(0,2)
d) (0,2)
To identify the solutions of the system of equations, we need to find the values of x and y that satisfy both equations simultaneously. Let's solve the system of equations step by step.
First, we'll rewrite the second equation in terms of x and y to make it easier to work with:
y = 2 - x
Now, we can substitute this expression for y into the first equation:
2x + 5(2 - x) = 10
Next, simplify the equation:
2x + 10 - 5x = 10
-3x + 10 = 10
-3x = 0
x = 0
Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y. Let's use the second equation:
y = 2 - x
y = 2 - 0
y = 2
Therefore, the solution to the system of equations is (x, y) = (0, 2).
Looking at the answer choices provided:
a) (-2, 0) does not satisfy the second equation, y = 2 - x
b) (2, 0) does not satisfy the first equation, 2x + 5y = 10
c) (0, -2) does not satisfy the first equation, 2x + 5y = 10
d) (0, 2) satisfies both equations, 2x + 5y = 10 and y = 2 - x
Therefore, the solution to the system of equations is (x, y) = (0, 2), which corresponds to option d).