Call the number of hours babysitting
and the number of hours walking dogs
.
We know that she earns $6/hr for babysitting or
, and $5/hr walking dogs or
. We also know the total money is $43 and the total time is 8hours. Therefore:
To solve: First rearrange equation 1 to solve for either
or
(doesn't matter which, I'll use
):
Now substitute into equation 2:
and solve for
Now backsubstitute to solve for
:
She babysat for 3 hours and walked dogs for 5.
To check our work:
CHECKS
The graphs are identical and intersect at infinitely many points.
This is because 2(2x+3) is the same as 4x+6
Distribute the outer 2 to each term inside
2 times 2x = 4x
2 times 3 = 6
So 2(2x+3) simplifies to 4x+6
Or you can think of 4x+6 factoring to 2(2x+3)
Answer:
The answer is
x
=
7
and
x
=
2
.
Factor the left side of the equation.
(
x
−
7
)
(
x
−
2
)
=
0
Solve each term in the product separately.
x
−
7
=
0
Add 7 to both sides.
x
=
7
x
−
2
=
0
Add 2 to both sides.
x
=
2
Check.
x
=
7
7
2
−
9
(
7
)
+
14
=
0
49
−
63
+
14
=
0
x
=
2
2
2
−
9
(
2
)
+
14
=
0
4
−
18
+
14
=
0
Answer link
Related questions
What are the different methods for solving quadratic equations?
What would be the best method to solve
−
3
x
2
+
12
x
+
1
=
0
?
How do you solve
−
4
x
2
+
4
x
=
9
?
What are the two numbers if the product of two consecutive integers is 72?
Which method do you use to solve the quadratic equation
81
x
2
+
1
=
0
?
How do you solve
−
4
x
2
+
4000
x
=
0
?
How do you solve for x in
x
2
−
6
x
+
4
=
0
?
How do you solve
x
2
−
6
x
−
16
=
0
by factoring?
How do you solve by factoring and using the principle of zero products
x
2
+
7
x
+
6
=
0
?
How do you solve
x
2
=
2
x
?
See all questions in Comparing Methods for Solving Quadratics
Impact of this question
44315 views around the world
You can reuse this answer
Creative Commons License
iOS
Android
Privacy
Terms
Step-by-step explanation:
Answer: are there choices?
Step-by-step explanation:
Answer:
(3,2)
Step-by-step explanation:
2x-4=y
2y+3x=13
We substitute the y in. They already gave us the equation 2x-4=y simplified so you would just plug this into the other equation
2(2x-4) +3x=13 : *distribute*
4x-8+3x=13 : *combine like terms*
7x-8=13 * add the 8 to the other side*
7x=21 *divide*
x=3
So the y=2x-4 is what we added in the place of the y to subtract it and solve for x. The second step would be solving for y. So now that we have our answer, 3 we plug it into the other equation preferably.
2(3)-4 =y : 6-4=y : 2=y
We can check our answer by pugging both x and y into both equations to make sure they are right. The statement should be true.
2x-4=y 2(3)-4=(2) 2=2
2y+3x=13 2(2)+3(3)=13 13=13