$$ \left\{\begin{array}{r}y=-2 x+6 \ y=-x+4\end{array}\right. $$ Graph the system.

Question

UpStudy AI · Accepted Answer

It seems that I cannot directly plot the equations at the moment. However, I can guide you through the process of graphing the system of equations step by step.

### Step 1: Identify the equations
The system of equations is:
1. $$ y = -2x + 6 $$
2. $$ y = -x + 4 $$

### Step 2: Find the intercepts
For each equation, we can find the y-intercept and x-intercept.

**For the first equation $$ y = -2x + 6 $$:**
- **Y-intercept**: Set $$ x = 0 $$:
  $$
  y = -2(0) + 6 = 6 \quad \text{(Point: (0, 6))}
  $$
- **X-intercept**: Set $$ y = 0 $$:
  $$
  0 = -2x + 6 \implies 2x = 6 \implies x = 3 \quad \text{(Point: (3, 0))}
  $$

**For the second equation $$ y = -x + 4 $$:**
- **Y-intercept**: Set $$ x = 0 $$:
  $$
  y = -0 + 4 = 4 \quad \text{(Point: (0, 4))}
  $$
- **X-intercept**: Set $$ y = 0 $$:
  $$
  0 = -x + 4 \implies x = 4 \quad \text{(Point: (4, 0))}
  $$

### Step 3: Plot the points
Now, you can plot the points on a graph:
- For the first equation, plot the points (0, 6) and (3, 0).
- For the second equation, plot the points (0, 4) and (4, 0).

### Step 4: Draw the lines
Connect the points for each equation to form straight lines. The first line will slope downwards from left to right, and the second line will also slope downwards but at a different angle.

### Step 5: Find the intersection point
To find the intersection point of the two lines, set the equations equal to each other:
$$
-2x + 6 = -x + 4
$$
Solving for $$ x $$:
$$
-2x + x = 4 - 6 \implies -x = -2 \implies x = 2
$$
Now substitute $$ x = 2 $$ back into either equation to find $$ y $$:
$$
y = -2(2) + 6 = 2
$$
Thus, the intersection point is $$ (2, 2) $$.

### Summary
- The lines intersect at the point $$ (2, 2) $$.
- You can graph the lines using the points and slopes described above.

If you have graphing software or a graphing calculator, you can input the equations directly to visualize them.
To graph the system of equations: 1. $$ y = -2x + 6 $$ 2. $$ y = -x + 4 $$ - Plot the y-intercepts: (0,6) and (0,4). - Plot the x-intercepts: (3,0) and (4,0). - Draw the lines through these points. - The lines intersect at (2,2). No further assistance needed for graphing.

Graph the system.

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Algebra Questions