Question

the school store sells binders for $4.00 each and pens for $2.00 each the equation in standard form is 4x+2y=20 it describes the number of binders x and pens y that you can buy for $20complete the table to show the possible combinations of binders and pens that can be bought for $20I really need help

Answer 1

(0,10), (1,8), (2,6), (3,4), (5,2), (6,-2)

Explanation

$4x+2y=20$

Step 1

subtract 4x in both sides

$\begin{gathered} 4x+2y=20 \\ 4x+2y-4x=20-4x \\ 2y=20-4x \end{gathered}$

Step 2

divide each side by 2

$\begin{gathered} \frac{2y}{2}=\frac{20}{2}-\frac{4x}{2} \\ y=\text{ 10-2x Equation(1)} \end{gathered}$

Step 3

replace the value of x in equation (1) starting with 0 (table)

$\begin{gathered} \text{when x=0} \\ y=10-2x=10-2(0)=10-0=10 \\ \text{then, when x= 0, y=}10 \end{gathered}$

point(0,10)

$\begin{gathered} \text{when x= 1} \\ y=10-2x=10-2(1)=10-2=8 \\ (1,8) \end{gathered}$

point(1,8)

$\begin{gathered} f(1)=10-2(1)=10-2=8 \\ f(2)=10-2(2)=10-4=6 \\ f(3)=10-2(3)=10-6=4 \\ f(4)=10-2(4)=10-8=2 \\ f(5)=10-2(5)=10-10=0 \\ f(6)=10-2(6)=10-12=-2 \end{gathered}$

I hope this helps you