Question

question 2 of 10, step 1 of 1
correct
solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, or an infinite number of solutions. if the system has one solution, find the solution.
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$$\begin{cases} 3x + y = 22 \\\\ 2y = -6x + 44 \\end{cases}$$

answer
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\bigcirc one solution \qquad (\boxed{\quad}, \boxed{\quad})
\bigcirc no solution
\bigcirc infinite number of solutions

Explanation:

Step1: Solve first equation for y

From \(3x + y = 22\), we get \(y = 22 - 3x\).

Step2: Substitute y into second equation

Substitute \(y = 22 - 3x\) into \(2y = -6x + 44\):
\(2(22 - 3x) = -6x + 44\)
Expand left side: \(44 - 6x = -6x + 44\)
Add \(6x\) to both sides: \(44 = 44\).
This is a true statement, meaning the equations are dependent (same line), so there are infinite solutions.

Answer:

Infinite Number of Solutions