An employee has two hourly wage options for positions in a large corporation. One position pays $11.00 plus additional unit rate of $0.50 unit produced. The other pays $7.25 plus a unit rate of $1.25.

W(x)=11+0.5x
M(x)=7.25+1.25x
I need to find the solution for the systems by either using substitution or combination/elimination

try making both equations equal to each other W(x)=M(x) and simplify

You mean where is the breakeven point where the two jobs pay equally?

let W = M and substitute
11 + .5 x = 7.25 + 1.25 x
3.75 = .75 x
x = 5 units
the M = W = 11 + 2.5 = $13.5

To find the solution for the given system of equations using substitution or elimination, we need to equate the two equations and solve for the variable 'x'.

Let's use the substitution method first.

1. Substitute the expression for 'W(x)' into the second equation:
M(x) = 7.25 + 1.25x
W(x) = 11 + 0.5x

Now we can substitute 'W(x)' into 'M(x)':
7.25 + 1.25x = 11 + 0.5x

2. Simplify the equation by combining like terms:
1.25x - 0.5x = 11 - 7.25

This gives us:
0.75x = 3.75

3. Now, solve for 'x' by dividing both sides of the equation by 0.75:
x = 3.75 / 0.75
x = 5

So, the value of 'x' is 5.

4. To find the corresponding values of 'W(x)' and 'M(x)', substitute the value of 'x' back into either equation:
W(x) = 11 + 0.5x
W(5) = 11 + 0.5(5)
W(5) = 11 + 2.5
W(5) = 13.5

Therefore, the wage for the position with the hourly wage options is $13.50 per hour.

Similarly, to find the value of 'M(x)':
M(x) = 7.25 + 1.25x
M(5) = 7.25 + 1.25(5)
M(5) = 7.25 + 6.25
M(5) = 13.50

Thus, the wage for the position with the unit rate of $1.25 is also $13.50 per hour.

Therefore, both positions will have the same wage of $13.50 per hour.