Question

Solving Equations Using Substitution Quick Check
5 of 55 of 5 Items








Question
How many solution(s) does the system of equations have?
−5x+y=−18

10x−2y=36
(1 point)
Responses

infinite
infinite

two
two

none
none

one

Answer 1

To determine the number of solutions in the system of equations given:

1. \( -5x + y = -18 \) (Equation 1)
2. \( 10x - 2y = 36 \) (Equation 2)

We can solve these equations to either find a unique solution, find no solutions, or find infinitely many solutions.

First, let's rearrange Equation 1 to solve for \( y \):

\[
y = 5x - 18
\]

Now we can substitute this expression for \( y \) into Equation 2:

\[
10x - 2(5x - 18) = 36
\]

Simplifying this:

\[
10x - 10x + 36 = 36
\]

This simplifies to:

\[
36 = 36
\]

This is a true statement, meaning that the two equations represent the same line. Therefore, there are infinitely many solutions to the system.

The answer is: **infinite**.