Answer:
see explanation
Step-by-step explanation:
(10)
let x represent blueberry pie and y blackberry pie, then
x + 2y = 53 → (1)
10x + 3y = 224 → (2)
Multiplying (1) by - 10 and adding to (2) will eliminate x
- 10x - 20y = - 530 → (3)
Add (2) and (3) term by term to eliminate x
0 - 17y = - 306
- 17y = - 306 ( divide both sides by - 17 )
y = 18
Substitute y = 18 into either of the 2 equations and solve for x
Substituting into (1)
x + 2(18) = 53
x + 36 = 53 ( subtract 36 from both sides )
x = 17
Then
the cost of 1 blueberry pie is $17 and 1 blackberry pie is $18
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The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Calculate m using the slope formula
(11)
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 2) and (x₂, y₂ ) = (0, 3)
m = [tex]\frac{3-2}{0-4}[/tex] = - [tex]\frac{1}{4}[/tex]
The line crosses the y- axis at (0, 3 ) ⇒ b = 3
y = - [tex]\frac{1}{4}[/tex] x + 3 ← equation of line
(12)
(x₁, y₁ ) = (- 3, 1) and (x₂, y₂ ) = (4, 2)
m = [tex]\frac{2-1}{4+3}[/tex] = [tex]\frac{1}{7}[/tex] , then
y = [tex]\frac{1}{7}[/tex] x + b ← is the partial equation
To find b substitute either of the 2 points into the partial equation
Using (3, 1 ), then
1 = [tex]\frac{3}{7}[/tex] + b ⇒ b = 1 - [tex]\frac{3}{7}[/tex] = [tex]\frac{4}{7}[/tex]
y = [tex]\frac{1}{7}[/tex] x + [tex]\frac{4}{7}[/tex] ← equation of line
