Question

NEED ANSWER ASAP

Solve the system of equations using the linear combination method. {c+d=17c−d=3 Enter your answers in the boxes. c = d =

Answer 1

Answer: c = 10, d = 7

Explanation:

To solve this system using the linear combination method, we want to eliminate one of the variables, either c or d, by adding or subtracting the two equations. One way to do this is to add the two equations together, which will cancel out the d terms:

(c + d) + (c - d) = 17 + 3

2c = 20

c = 10

Now we can substitute this value of c into either equation to solve for d:

c - d = 3

10 - d = 3

d = 7

Therefore, the solution to the system is:

c = 10, d = 7.

Answer 2

c=10 and d=7

Explanation:

Use linear combination to solve the following system of equations.

Linear combination is synonymous with the method of elimination. The goal of elimination is to "eliminate" one of the variables so that we may solve for the other.

`\left\{\begin{array}{ccc}c+d=17\\c-d=3\end{array}\right`

Notice how the "d" term has opposite signs in the system. We can add these two equations together to "eliminate" d.

`(c+d=17)+(c-d=3)=\boxed{2c=20}\\\\\therefore \boxed{\boxed{c=10}}`

We now know what "c" equals, plug this value into either of the equations and solve for "d."

`c=10\\\\\Longrightarrow 10+d=17\\\\\therefore \boxed{\boxed{d=7}}`

Thus, the system is solved. c=10 and d=7.