Questions: Solving Systems of Linear Equations by graphing: 6x+3y=6 4x+2y=-18 Rewrite 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 One Solution ( ) No Solution Infinite Number of Solutions

Solving Systems of Linear Equations by graphing:
6x+3y=6
4x+2y=-18
Rewrite 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
One Solution ( )
No Solution
Infinite Number of Solutions

Transcript text: Solving Systems of Linear Equations by graphing: \[ \begin{array}{l} 6 x+3 y=6 \\ 4 x+2 y=-18 \end{array} \] Rewrite the linear equations by writing the equations in slope-intercept form: \[ \begin{array}{l} y=\square x+\square \\ y=\square x+\square \end{array} \] Identify the appropriate number of solutions. If there is a solution, give the One Solution ( $\square$ ) No Solution Infinite Number of Solutions

Solution

Solution Steps

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

The first equation is $6x + 3y = 6$. To convert to slope-intercept form, isolate $y$. $3y = -6x + 6$ $y = -2x + 2$

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

The second equation is $4x + 2y = -18$. To convert to slope-intercept form, isolate $y$. $2y = -4x - 18$ $y = -2x - 9$

Step 3: Determine the number of solutions.

Both equations are now in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. First equation: $y = -2x + 2$, so $m = -2$ and $b = 2$. Second equation: $y = -2x - 9$, so $m=-2$ and $b = -9$. Since the slopes are equal and the y-intercepts are different, the lines are parallel and will never intersect. Therefore, there is no solution.