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9180ced33ffb791aefc965fe8e2ca5
(Level 3)
nalty: none
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system of equations using elimination:
8x+3y=1 and
6x+4y=6.
Attempt 1 out of 2
)
Submit Answer

$9180$ ced $33$ ffb $791$ aefc $965$ fe $8$ e $2$ ca $5$ $\newline$ (Level $3$ ) $\newline$ nalty: none $\newline$ Watch Video $\newline$ Show Examples $\newline$ system of equations using elimination: $8 x+3 y=1$ and $6 x+4 y=6$ . $\newline$ Attempt $1$ out of $2$ $\newline$ ) $\newline$ Submit Answer

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Solve a system of equations using elimination: word problems

Full solution

Q.

9180

ced

33

ffb

791

aefc

965

fe

8

e

2

ca

5

\newline

(Level

3

)

\newline

nalty: none

\newline

Watch Video

\newline

Show Examples

\newline

system of equations using elimination:

8 x+3 y=1

and

6 x+4 y=6

.

\newline

Attempt

1

out of

2

\newline

)

\newline

Submit Answer

Define Variables: Let's call the price of a hot dog meal $h$ and the price of a hamburger meal $d$ . We have two equations: $3h + 2d = 32$ and $2h + d = 19$ .
Multiply Second Equation: To eliminate one variable, I'll multiply the second equation by $2$ to get $4h + 2d = 38$ .
Subtract Equations: Now, I'll subtract the first equation from the new second equation: $4h + 2d$ - $3h + 2d$ = ${38} - {32}$ , which simplifies to $h = 6$ .
Substitute $h=6$ : Substitute $h = 6$ into the first equation: $3(6) + 2d = 32$ . This simplifies to $18 + 2d = 32$ .
Solve for d: Subtract $18$ from both sides to solve for $d$ : $2d = 32 - 18$ , which gives $2d = 14$ .
Find $d$ : Divide both sides by $2$ to find $d$ : $d = \frac{14}{2}$ , which gives $d = 7$ .
Final Answer: So, hot dog meals cost $\$6$ each, and hamburger meals cost $\$7$ each.

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