Question

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.
\

$$\begin{cases} y = 4x - 23 \\\\ y = -9x + 29 \\end{cases}$$

answer
selecting an option will enable input for any required text boxes. if the selected option does not have any associated text boxes, then no further input is required.
\bigcirc one solution \quad (\boxed{\quad}, \boxed{\quad})
\bigcirc no solution
\bigcirc infinite number of solutions

Explanation:

Step1: Substitute y from first equation into second

Since \( y = 4x - 23 \) and \( y = -9x + 29 \), set them equal: \( 4x - 23 = -9x + 29 \)

Step2: Solve for x

Add \( 9x \) to both sides: \( 4x + 9x - 23 = 29 \) → \( 13x - 23 = 29 \)
Add 23 to both sides: \( 13x = 29 + 23 \) → \( 13x = 52 \)
Divide by 13: \( x = \frac{52}{13} = 4 \)

Step3: Find y using x = 4

Substitute \( x = 4 \) into \( y = 4x - 23 \): \( y = 4(4) - 23 = 16 - 23 = -7 \)

Answer:

One Solution \((4, -7)\)