The equations y = 10/5 - 0.4x and x = 5 - 5/2y are equivalent to 2x + 5y = 10.
Let's test each equation to see if it is equivalent to 2x + 5y = 10:
1 - y = (2/5)x + 2
Substitute y into the original equation:
2x + 5((2/5)x + 2) = 10
Simplify:
2x + 2x + 10 ≠ 10
Not equivalent.
2- x = 0.5 - 2.5y
Substitute x into the original equation:
2(0.5 - 2.5y) + 5y = 10
Simplify:
1 - 5y + 5y ≠ 10
Not equivalent.
3 - y = 10/5 - 0.4x
Simplify the right side:
y = 2 - 0.4x
Substitute y into the original equation:
2x + 5(2 - 0.4x) = 10
Simplify:
2x + 10 - 2x = 10
10 = 10
Equivalent.
4 - 2x = 10 - 5y
Solve for y:
y = 2 - 0.4x
Substitute y into the given equation:
2x = 10 - 5(2 - 0.4x)
Simplify:
2x = 10 - 10 + 2x
2x = 2x
Equivalent.
5 - -5y = 2x + 10
Divide both sides by -5:
y = -2/5x - 2
Not equivalent.
6 - x = 5 - 5/2y
Substitute x into the original equation:
2(5 - 5/2y) + 5y = 10
Simplify:
10 - 5y + 5y = 10
10 = 10
Equivalent.
Complete question:
Select all equations equivalent to 2x+5y=10
1: y = 2/5 x+2
2: x =.5 - 2.5y
3: y = 10/5 -0.4x
4: 2x = 10 - 5y
5: -5y = 2x + 10
6: x = 5 - 5/2 y