Answer:
p= 2.5
q= 7
Step-by-step explanation:
The lines should overlap to have infinite solutions, slopes should be same and y-intercepts should be same.
Equations in slope- intercept form:
6x-(2p-3)y-2q-3=0 ⇒ (2p-3)y= 6x -2q-3 ⇒ y= 6/(2p-3)x -(2q+3)/(2p-3)
12x-( 2p-1)y-5q+1=0 ⇒ (2p-1)y= 12x - 5q+1 ⇒ y=12/(2p-1)x - (5q-1)/(2p-1)
Slopes equal:
6/(2p-3)= 12/(2p-1)
6(2p-1)= 12(2p-3)
12p- 6= 24p - 36
12p= 30
p= 30/12
p= 2.5
y-intercepts equal:
(2q+3)/(2p-3)= (5q-1)/(2p-1)
(2q+3)/(2*2.5-3)= (5q-1)/(2*2.5-1)
(2q+3)/2= (5q-1)/4
4(2q+3)= 2(5q-1)
8q+12= 10q- 2
2q= 14
q= 7
Expressions can be represented as equations, and vice versa.
A possible situation is as follows:
<em>John is 15 years old, and his age is 3 more than 5 times his brother's age</em>
The equation is given as:
This means that:
- 15 represents John's age
- P represents his brother's age
- 5 and 3 are the constants that relate their ages
Read more about word equations at:
brainly.com/question/20518082
Since she bought 4 bags of 50 beads and 3 bags of 200 beads you only need to use two operations: multiply and add.
4 x 50 is 200
3 x 200 is 600
600 + 200 = 800
Mariah purchase 800 beads in total.
Answer:
Step-by-step explanation:
y = mx + b
we can see the slope is down hill, so it's negative
when the X is zero then it's 2
b = 2
slope is rise over run 2/3
y = -2/3x + 2
the slope is -2/3 (note the negative)
the y intercept is 2
Answer:
width = 18 cm
Step-by-step explanation:
perimeter of rectangle = 2(length + width)
then:
90 = 2(27+w)
90/2 = 27+w
w = width
45 = 27+w
45 - 27 = w
18 = w
Check:
90 = 2(27+18)
90 =2*45 =
