Solve the following system of linear equations by graphing:

4x+2y5x+y=24=30

It looks like there might be a typo in the system of linear equations you've provided. Based on your input, you might have intended to write something like:

1. \( 4x + 2y = 24 \)
2. \( 5x + y = 30 \)

Let me know if this is correct, or feel free to clarify further.

If this is correct, here's how you can solve the system by graphing:

### Step-by-Step Solution:

**Equation 1:**
\[
4x + 2y = 24
\]
Solve for \( y \):
\[
2y = -4x + 24
\]
\[
y = -2x + 12
\]
This is the slope-intercept form \( y = mx + b \), where the slope \( m = -2 \) and the y-intercept is 12.

**Equation 2:**
\[
5x + y = 30
\]
Solve for \( y \):
\[
y = -5x + 30
\]
This is also in the slope-intercept form, where the slope \( m = -5 \) and the y-intercept is 30.

### Graphing:

1. **Graph the first equation** \( y = -2x + 12 \):
   - Start by plotting the y-intercept at \( (0, 12) \).
   - From there, use the slope \( -2 \) (which means go down 2 units and right 1 unit) to find another point.

2. **Graph the second equation** \( y = -5x + 30 \):
   - Start by plotting the y-intercept at \( (0, 30) \).
   - Use the slope \( -5 \) (go down 5 units and right 1 unit) to find another point.

### Intersection:
The solution to the system of equations is the point where the two lines intersect. After plotting both lines, their intersection point represents the solution to the system.

Would you like me to plot the graph or show the intersection calculation?

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Let me know if you'd like more details, and if you have any questions!

### Related Questions:
1. How do you find the slope from a linear equation?
2. What happens if two lines are parallel when solving by graphing?
3. How can substitution or elimination be used to solve this system of equations?
4. How do you determine the y-intercept in a linear equation?
5. What are some real-life applications of solving systems of equations by graphing?

**Tip:** If two lines have the same slope but different y-intercepts, they are parallel and have no solution.

Solve the following system of linear equations by graphing: 4x + 2y = 24, 5x + y = 30

Learn how to solve the system of linear equations 4x + 2y = 24 and 5x + y = 30 by graphing. This solution covers key algebraic concepts, including converting to slope-intercept form and finding the point of intersection. Suitable for students in Grades 8-10.

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