3 x 13x1
minus−
x 2x2
equals=
negative 8−8
2 x 12x1
minus−
4 x 24x2
equals=
negative 2−2
Question content area bottom
Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The unique solution is x 1 equalsx1=enter your response here and x 2 equalsx2=enter your response here.
B.
The system has infinitely many solutions. The solution is x 1 equalsx1=enter your response here and x 2x2equals=t.
​(Simplify your answer. Type an expression using t as the​ variable.)
C.
There is no solution.

We are given a system of two linear equations with two variables \( x_1 \) and \( x_2 \). Let's break down the system:

\[
3x_1 - x_2 = -8
\]
\[
2x_1 - 4x_2 = -2
\]

### Step 1: Solve the system using substitution or elimination.

#### Method 1: Elimination

We have the following two equations:

1. \( 3x_1 - x_2 = -8 \)
2. \( 2x_1 - 4x_2 = -2 \)

Let's eliminate one of the variables by multiplying the first equation to match the second equation in terms of \( x_1 \).

Multiply the first equation by 2:

\[
2(3x_1 - x_2) = 2(-8)
\]
\[
6x_1 - 2x_2 = -16
\]

Now subtract the second equation from this:

\[
(6x_1 - 2x_2) - (2x_1 - 4x_2) = -16 - (-2)
\]
\[
(6x_1 - 2x_2 - 2x_1 + 4x_2) = -16 + 2
\]
\[
4x_1 + 2x_2 = -14
\]

This simplifies to:

\[
4x_1 + 2x_2 = -14
\]

This shows that there is an error in the solution method. I will

3x1 - x2 = -8; 2x1 - 4x2 = -2. Select the correct choice below: A. The unique solution is x1= and x2=. B. The system has infinitely many solutions. The solution is x1= and x2=t. C. There is no solution.

This webpage provides a step-by-step guide to solving the system of linear equations 3x1 - x2 = -8 and 2x1 - 4x2 = -2 using the elimination method. Learn key algebra concepts such as unique solutions, infinitely many solutions, and no solution scenarios. Ideal for students in Grades 9-10.

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