Final answer:
The solution to the system of equations y = x + 3 and 5y = -x + 9 can be found by graphing the lines. The first line has a slope of 1 and a y-intercept of 3, while the second line, when simplified, has a slope of -1/5 and a y-intercept of 9/5. The intersection point of the two graphs is the solution.
Step-by-step explanation:
The system of equations given are y = x + 3 and 5y = -x + 9. To find the solution, we can graph these equations using their slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. For the first equation, y = x + 3, the slope (m) is 1 and the y-intercept (b) is 3. You can construct a table of values by choosing different x-values and then calculating the corresponding y-values.
For the second equation, 5y = -x + 9, you can first transform it into slope-intercept form by dividing each term by 5, resulting in y = -1/5x + 9/5. The slope here is -1/5 and the y-intercept is 9/5. Again, you can create a table of x and y values to assist in graphing this line.
After plotting these lines on the coordinate plane, remember that the solution to the system of equations is the point where the two lines intersect. The y-intercept is where each line crosses the y-axis, and the slope is the rise over run for each line.