Hi there!
To solve this problem using substitution, we need to set x equal to a value and substitute it into the other equation.
Since
x - 4y = 5,
x = 5 + 4y
3x - 7y = 10
3(5 + 4y) - 7y = 10
15 + 12y - 7y = 10
15 + 5y = 10
5y = -5
y = -1
Now that we know y is -1, we can substitute it back into the equation to find x:
y = -1
x - 4y = 5
x - 4(-1) = 5
x - (-4) = 5
x + 4 = 5
x = 1
So, your answers are x = 1 and y = -1.
Hope this helps!
Answer:
104.4 for A.
Step-by-step explanation:
Answer:
Solid paper costs 1.75 each
Printed paper costs 2.50 each
Step-by-step explanation:
Given:
Ben = $43.50 (12 rolls solid paper and 9 rolls of printed paper)
Joel = $51.50 (8 rolls solid paper and 15 rolls of printed paper)
Let x = solid paper
Let y = printed paper
12x + 9y = 43.50
8x + 15y = 51.50
Find x:
8x + 15y = 51.50
8x = 51.50 - 15y
x = (51.50 - 15y)/8
Substitute x:
12x + 9y = 43.50
12(51.50 - 15y)/8 + 9y = 43.50
(618 - 180y)/8 + 9y = 43.50
8 (618 - 180y)/8 + 8*9y = 43.50 * 8
618 - 180y + 72y = 348
-108y = 348 - 618
-108y = -270
-108y/-108 = -270/-108
y = 2.50
x = (51.50 - 15y)/8
x = (51.50 - 15(2.5) /8
x = (51.50 - 37.50)/8
x = 14/8
x = 1.75
To check: x = 1.75 ; y = 2.5
12x + 9y = 43.50
12(1.75) + 9(2.5) = 43.50
21 + 22.50 = 43.50
43.50 = 43.50
8x + 15y = 51.50
8(1.75) + 15(2.5) = 51.50
14 + 37.50 = 51.50
51.50 = 51.50
Answer:
Step-by-step explanation:
Explanation:
First, find two points on the line if you change the inequality to an equation.
For
x
=
0
:
0
+
2
y
=
4
2
y
=
4
2
y
2
=
4
2
y
=
2
or
(
0
,
2
)
For
y
=
0
:
x
+
0
=
4
x
=
4
or
(
4
,
0
)
We can plot these two points and draw a line through them to get the border of the inequality:
graph{(x^2+(y-2)^2-0.075)((x-4)^2+y^2-0.075)(x+2y-4)=0}
The line will be solid because the inequality operator has a "or equal to" clause in it. We can now shade the area to the right of the line because the inequality has a "great than" clause in it.
graph{(x+2y-4)>=0}
