Questions: -4x + y = 12 -8x + 2y = 24 Graph the linear equations by writing the equations in slope-intercept form: y = x + y = x + Identify the appropriate number of solutions. If there is a solution, give the point: One Solution ( , )

-4x + y = 12
-8x + 2y = 24

Graph the linear equations by writing the equations in slope-intercept form:
y = x +
y = x +

Identify the appropriate number of solutions. If there is a solution, give the point:
One Solution ( , )

Transcript text: \[ \begin{array}{r} -4 x+y=12 \\ -8 x+2 y=24 \end{array} \] Graph the linear equations by writing the equations in slope-intercept form: \[ \begin{array}{l} y=x+ \\ y=\quad x+ \end{array} \] Identify the appropriate number of solutions. If there is a solution, give the point: One Solution ( $\qquad$ , $\qquad$ )

Solution

Solution Steps

Step 1: Convert the first equation to slope-intercept form

The first equation is $-4x + y = 12$. To convert it to slope-intercept form ($y = mx + b$), solve for $y$:

\[ -4x + y = 12 \implies y = 4x + 12 \]

Step 2: Convert the second equation to slope-intercept form

The second equation is $-8x + 2y = 24$. To convert it to slope-intercept form ($y = mx + b$), solve for $y$:

\[ -8x + 2y = 24 \implies 2y = 8x + 24 \implies y = 4x + 12 \]

Step 3: Identify the number of solutions

Both equations are $y = 4x + 12$. Since they are identical, they represent the same line. Therefore, there are infinitely many solutions, as every point on the line is a solution.