Questions: y=3x+4 y=(1/2)x-1

y=3x+4 y=(1/2)x-1
Transcript text: 18) \[ \begin{array}{l} y=3 x+4 \\ y=\frac{1}{2} x-1 \end{array} \]
failed

Solution

failed
failed

Solution Steps

Step 1: Find the intersection point

We are looking for the solution to the system of equations: \begin{align_} \label{eq:1} y &= 3x + 4 \\ y &= \frac{1}{2}x - 1\end{align_} We can set the two expressions for \(y\) equal to each other: \[3x + 4 = \frac{1}{2}x - 1\]

Step 2: Solve for x

Subtract \(\frac{1}{2}x\) from both sides: \[\frac{5}{2}x + 4 = -1\] Subtract 4 from both sides: \[\frac{5}{2}x = -5\] Multiply both sides by \(\frac{2}{5}\): \[x = -5 \cdot \frac{2}{5} = -2\]

Step 3: Solve for y

Substitute \(x = -2\) into the first equation: \[y = 3(-2) + 4 = -6 + 4 = -2\] Substitute \(x = -2\) into the second equation: \[y = \frac{1}{2}(-2) - 1 = -1 - 1 = -2\]

Final Answer

The solution is \(\boxed{x = -2, y = -2}\). The lines intersect at the point \((-2, -2)\).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Which ordered pair is a solution to the system of inequalities graphed here? A. (4,-2) B. (2,2) C. (-2,-2) D. (-6,2)
failedAnswered
MotoWin Auto Superstore is thinking about offering a two-year limited warranty for 928 on all new cars of a certain model. The terms of the warranty would be that MotoWin would replace the car free of charge under certain, specified conditions. Replacing the car in this way would cost MotoWin 13,800. Suppose that under the warranty, there is a 7% chance that MotoWin would have to replace the car one time and a 93% chance they wouldn't have to replace the car. If MotoWin knows that it will sell many of these warranties, should it expect to make or lose money from offering them? How much? To answer, take into account the price of the warranty and the expected value of the cost from replacing the car. MotoWin can expect to make money from offering these warranties. In the long run, they should expect to make dollars on each warranty sold. MotoWin can expect to lose money from offering these warranties. In the long run, they should expect to lose dollars on each warranty sold. MotoWin should expect to neither make nor lose money from offering these warranties.
failedAnswered
Mrs. Isaac comes to the emergency department complaining of difficulty breathing. An objective finding of dyspnea might include: Use of accessory muscles of respiration
failedAnswered
angle 6 congruent to angle 7
failedAnswered
Use the product rule to find the derivative. y=(4x^2+3)(2x-3) y'=