The supply and demand linear models of T-shirts for sale at a concert are represented by the following system of equations, where x is the quantity and y is the price:𝑦=150𝑥+4y= 501 x+4𝑦=−125𝑥+40y= 25−1 x+40Find the solution to the system
Question
The supply and demand linear models of T-shirts for sale at a concert are represented by the following system of equations, where x is the quantity and y is the price:𝑦=150𝑥+4y= 501 x+4𝑦=−125𝑥+40y= 25−1 x+40Find the solution to the system
Solution
The given system of equations is:
y = 150x + 4 y = -125x + 40
To find the solution to the system, we need to find the values of x and y that satisfy both equations. We can do this by setting the two equations equal to each other and solving for x:
150x + 4 = -125x + 40
Combine like terms:
275x + 4 = 40
Subtract 4 from both sides:
275x = 36
Divide both sides by 275:
x = 36/275 ≈ 0.131
Substitute x = 0.131 into the first equation to solve for y:
y = 150(0.131) + 4 ≈ 23.65
So, the solution to the system is x ≈ 0.131 and y ≈ 23.65.
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