Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Substitute teachers with Weston School District get paid by the day, although subs with teaching credentials earn a different amount than subs without credentials. Yesterday, 6 non-credentialed subs and 3 credentialed subs taught in the district. That cost the district $756. Today, 11 non-credentialed subs and 3 credentialed subs taught, receiving $1,151 from the district. How much do subs get paid?Subs without credentials get paid $_____ per day, and subs with credentials get paid $_____ per day.
Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Substitute teachers with Weston School District get paid by the day, although subs with teaching credentials earn a different amount than subs without credentials. Yesterday, 6 non-credentialed subs and 3 credentialed subs taught in the district. That cost the district $756. Today, 11 non-credentialed subs and 3 credentialed subs taught, receiving $1,151 from the district. How much do subs get paid?Subs without credentials get paid $_____ per day, and subs with credentials get paid $_____ per day.
Write Equations: Let's denote the daily pay for non-credentialed subs as x dollars and for credentialed subs as y dollars. We can write two equations based on the given information:For yesterday:6x+3y=756 (Equation 1)For today:11x+3y=1151 (Equation 2)We will use the elimination method to solve this system of equations.
Eliminate y: First, we will multiply Equation 1 by −1 to help eliminate the y variable when we add it to Equation 2.−1×(6x+3y)=−1×756−6x−3y=−756 (Equation 3)Now we have:−6x−3y=−75611x+3y=1151
Add Equations: Next, we add Equation 3 to Equation 2 to eliminate y.(−6x−3y)+(11x+3y)=(−756)+1151−6x+11x=1151−7565x=395
Solve for x: Now we solve for x by dividing both sides of the equation by 5.55x=5395x=79So, non-credentialed subs get paid $79 per day.
Substitute x: We will now substitute the value of x back into Equation 1 to solve for y.6(79)+3y=756474+3y=756
Solve for y: Subtract 474 from both sides of the equation to solve for y.3y=756−4743y=282
Solve for y: Subtract 474 from both sides of the equation to solve for y.3y=756−4743y=282 Finally, divide both sides by 3 to find the value of y.33y=3282y=94So, credentialed subs get paid $94 per day.
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