Answer: For the system given, there is no solution.
The slopes are the same for both equations, so the lines are parallel. With no intersection, there is no solution.
It may be easier to graph the system if you change the equations to slope intercept form y = mx + b
That locates the y-intercept, <em><u>b</u></em> and you can use the slope, <em><u>m</u></em> to plot additional points to draw the lines.
The attachment shows the graph of this system of equations.
Step-by-step explanation: Isolate y on the left
<u>First equation:</u>
4x + 6y = -12 Subtract 4x from both sides
6y = -4x -12 Divide both sides by 6
y = -4x/6 -12/6 Simplify
y = -2x/3 - 2 The y-intercept is -2, <u>the slope is -2/3</u>
<u>Second equation:</u>
2x + 3y = 6 Subtract 2x from both sides
3y = –2x + 6 . Divide both sides by 3
y = –2x/3 + 6/3 Simplify
y = –2x/3 +2 The y-intercept is -2, <u>the slope is -2/3 </u>
At this point we see that the slopes are the same, so the lines are parallel.
Answer:
The values of and
for a linear system with infinitely many solutions are -2 and 5, respectively.
Step-by-step explanation:
Let , if this linear system has infinitely many solutions, then the following conditions must be met:
and
.
and
The values of and
for a linear system with infinitely many solutions are -2 and 5, respectively.
Answer:
The mean, μ is 2.5063 and
The standard deviation, σ = 2.0499 × 10⁻²
Step-by-step explanation:
Here we have
and
10% have length < 2.48 in while
5% have length > 2.54 in
and
From the z score table
Critical z at 10% to the left = -1.282
Critical z at 5% to the right = 1.645
Therefore, the equations become
-1.282σ = 2.48 - μ → μ -1.282σ = 2.48
1.645σ = 2.54 - μ → μ + 1.645σ = 2.54
Solving the above equations gives
The mean, μ = 2.5063 and
The standard deviation, σ = 2.0499 × 10⁻².