Respuesta :
In this problem, we are going to write and solve a system of equations based on a real world situation.
Last week, she did 1 load of laundry and 8 loads of dishes, and her parents paid her $26. The week before, she finished 3 loads of laundry and 8 loads of dishes, earning a total of $30.
To begin, we need to create variables for the unknown cost of each chore.
Let x represent laundry, and let y represent dishes.
From the first equation, we can write the equation:
[tex]x+8y=26[/tex]We can write the second equation as:
[tex]3x+8y=30[/tex]Together, we have the system:
[tex]\begin{cases}x+8y={26} \\ 3x+8y={30}\end{cases}[/tex]Multiply the first equation by -1, then add it to the second equation:
[tex]\begin{gathered} \begin{cases}-1(x+8y={26)} \\ 3x+8y={30}\end{cases} \\ \\ \begin{cases}-x-8y={-26} \\ 3x+8y={30}\end{cases} \\ \\ (-x+3x)+(-8y+8y)=-26+30 \\ 2x=4 \end{gathered}[/tex]We can divide the remaining equation by 2 on both sides:
[tex]\begin{gathered} \frac{2x}{2}=\frac{4}{2} \\ \\ x=2 \end{gathered}[/tex]Lada made $2 per load of laundry.
We can use the value of x in the first equation to find the value of y. Substitute x = 2:
[tex]2+8y=26[/tex]Subtract 2 from both sides:
[tex]8y=24[/tex]Divide by 8 on both sides:
[tex]y=3[/tex]Lada made $3 per load of dishes.
