![6 = - 4x + y \\ - 5x - y = 21](https://tex.z-dn.net/?f=6%20%3D%20%20-%204x%20%2B%20y%20%5C%5C%20%20-%205x%20-%20y%20%3D%2021)
Solve the first equation for y
![y = 4x + 6 \\ - 5x - y = 21](https://tex.z-dn.net/?f=y%20%3D%204x%20%2B%206%20%5C%5C%20%20-%205x%20-%20y%20%3D%2021)
Substitute the given value of y into the equation -5x-y=21
![- 5x - (4x + 6) = 21](https://tex.z-dn.net/?f=%20-%205x%20-%20%284x%20%20%2B%20%206%29%20%3D%2021)
When there is a - in front of an expression in parentheses, change the sign of each term in the expression
![- 5x - 4x - 6 = 21](https://tex.z-dn.net/?f=%20-%205x%20-%204x%20-%206%20%3D%2021)
Collect like terms
![- 9x - 6 = 21](https://tex.z-dn.net/?f=%20-%209x%20-%206%20%3D%2021)
Move the constant to the right-hand side and change its sign
![- 9x = 21 + 6](https://tex.z-dn.net/?f=%20-%209x%20%3D%2021%20%2B%206)
Add the numbers
![- 9x = 27](https://tex.z-dn.net/?f=%20-%209x%20%3D%2027)
Divide both sides of equation by -3
![x = - 3](https://tex.z-dn.net/?f=x%20%3D%20%20-%203)
Substitute the given value of x into the equation y=4x+6
![y = 4 \times ( - 3) + 6](https://tex.z-dn.net/?f=y%20%3D%204%20%5Ctimes%20%28%20-%203%29%20%2B%206)
Multiply the numbers
![y = - 12 + 6](https://tex.z-dn.net/?f=y%20%3D%20%20-%2012%20%2B%206)
Calculate the difference
![y = - 6](https://tex.z-dn.net/?f=y%20%3D%20%20-%206)
The possible solution of the system is the ordered pair (x,y)
![(x,y)=(-3,-6)](https://tex.z-dn.net/?f=%28x%2Cy%29%3D%28-3%2C-6%29)
Answer:
=7/9
Step-by-step explanation:
To find the slope, we use the formula
m= (y2-y1)/ (x2-x1)
= (59-73)/(58-76)
=-14/-18
Divide top and bottom by 2
=7/9
{-1,-3,-7,-9}
hope it helps
84 pounds of Type B coffee is used
<em><u>Solution:</u></em>
Let "x" be the pounds of type A coffee
Let "y" be the pounds of type B coffee
Cost per pound of type A = $ 5.50
Cost per pound of Type B = $ 4.20
<em><u>This month, Chau made 143 pounds of the blend</u></em>
x + y = 143
x = 143 - y -------- eqn 1
<em><u>For a total cost of $677.30. Thus we frame a equation as:</u></em>
pounds of type A coffee x Cost per pound of type A + pounds of type B coffee x Cost per pound of Type B = 677.30
![x \times 5.50 + y \times 4.20 = 677.30\\\\5.5x + 4.2y = 677.30 -------- eqn 2](https://tex.z-dn.net/?f=x%20%5Ctimes%205.50%20%2B%20y%20%5Ctimes%204.20%20%3D%20677.30%5C%5C%5C%5C5.5x%20%2B%204.2y%20%3D%20677.30%20--------%20eqn%202)
<em><u>Let us solve eqn 1 and eqn 2</u></em>
<em><u>Substitute eqn 1 in eqn 2</u></em>
![5.5(143-y) +4.2y = 677.30\\\\786.5 -5.5y + 4.2y = 677.30\\\\5.5y - 4.2y = 786.5 - 677.30\\\\1.3y = 109.2\\\\Divide\ both\ sides\ by\ 1.3\\\\y = 84](https://tex.z-dn.net/?f=5.5%28143-y%29%20%2B4.2y%20%3D%20677.30%5C%5C%5C%5C786.5%20-5.5y%20%2B%204.2y%20%3D%20677.30%5C%5C%5C%5C5.5y%20-%204.2y%20%3D%20786.5%20-%20677.30%5C%5C%5C%5C1.3y%20%3D%20109.2%5C%5C%5C%5CDivide%5C%20both%5C%20sides%5C%20by%5C%201.3%5C%5C%5C%5Cy%20%3D%2084)
Thus 84 pounds of Type B coffee is used