Question

PLEASE NEED HELP NOW WILL GIVE MEDAL AND FANPLLLEEAASSEE NEED HELP NOW WILL GIVE MEDAL3. Solve the system of equations using linear combination.
a+c=9
8a+4.5c=58

Answer 1

Are you familiar with elimination and substitution method?

Answer 2

no I need someone to walk me through the entire problem

Answer 3

Okay no worries (:

So when solving systems of linear equation, there are two methods that we can use: Substitution method where you rearrange one equation in terms of variable and substituting it with the second equation.
Elimination method is when you manipulate one equation and add it to the second equation in order to eliminate one variable.

Do for your question, which method do you want to use?

Answer 4

Substitution

Answer 5

@Data_LG2

Answer 6

okay great! So here's how we do it:

\(\sf a+ \color{red}{c}=9\) this will be our equation 1

\(\sf 8a+4.5\color{red}{c}=58\) this will be our equation 2

we want to solve for 'a'
so we have to rearrange equation 1, in terms of \(\color{red}{c}\)
can you do it?
if you rearrange eqn 1, you'll get

\(\color{red}{c}= \)

Answer 7

9-a

Answer 8

yes right!
\(\sf \color{red}{c= 9-a}\) this will be our new equation 1

Now the next step is to put equation on inside equation 2 to solve for a
To do that, we replace \(\color{red}{c}\) in the equation 2 with our equation 1.

\(\sf 8a+4.5\color{red}{c}=58\\8a+4.5 (\color{red}{9-a}) = 58\)

is it clear so far?

Answer 9

yes

Answer 10

good.

So if we solve for a in our new combined equation: \(\sf 8a+4.5 (\color{red}{9-a}) = 58\)
what will you get for a ?

Answer 11

3.5a=58

Answer 12

so a=16.57

Answer 13

so now we plug in a in the first equation and solve for c

Answer 14

??

Answer 15

almost right! but remember the bracket part: