2-Variable Equations & Inequalities Online Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
11 of 1811 of 18 Items

Question
Use the substitution method to solve the system x−2y=3
, 4x−8y=12
.(1 point)
Responses

(3,0)
left parenthesis 3 comma 0 right parenthesis

(0,3)
left parenthesis 0 comma 3 right parenthesis

infinite solutions
infinite solutions

no solution
no solution
Remaining Attempts : 3

Answer 1

To solve the system of equations using the substitution method, we start with the given equations:

1. \( x - 2y = 3 \) (Equation 1)
2. \( 4x - 8y = 12 \) (Equation 2)

We’ll first solve one of the equations for one variable and substitute it into the other equation. Let's solve Equation 1 for \( x \):

From Equation 1: \[ x = 2y + 3 \]

Next, we can substitute this expression for \( x \) into Equation 2:

\[ 4(2y + 3) - 8y = 12 \]

Now, let's simplify this equation:

\[ 8y + 12 - 8y = 12 \]

The \( 8y \) terms cancel out: \[ 12 = 12 \]

This statement is always true, indicating that the two equations are dependent. Thus, they represent the same line, which means there are infinite solutions.

So, the correct response is:

infinite solutions