can someone show me how to do it step by step please!

Use a graph and table to solve each system. check your answer
{y+x=5
{3x-5y=-1

x + y = 5,

3x - 5y = -1,
I will use the elimination method which
eliminates 1 variable and allows me to solve for the other.

Step 1. Multiply both sides of the 1st Eq by -3 and add the 2 Eqs:

-3x - 3y = -15,
3x - 5y = -1,

0 - 8y = -16,
- 8y = - 16,

Step 2. Divide both sides by -8 and get:
y = 2.

Step 3. Substitute 2 for y in Eq 1
and solve for x:
x + 2 - 5,
x = 5 - 2,
x = 3.

Solution set:(x , y) = (3 , 2) = The
point where the 2 graphs will intersect.

To graph the Eqs, use the following
convenient points:

x + y = 5. (0 , 5) , (2 , 3) , (5 ,0).
3x - 5y = -1. (-2 , -1) , (3 , 2) ,
(5 , 3.2).

I hope this will help.

CORRECTION: The 1st Eq under Step 3

should read: x + 2 = 5.

Sure! Let's solve the system of equations step by step using a graph and a table.

Step 1: Solve the first equation for y in terms of x.
We have the equation: y + x = 5.
To solve for y, subtract x from both sides:
y = 5 - x.

Step 2: Create a table of values.
Choose some x-values and substitute them into the equation y = 5 - x to find the corresponding y-values. Let's choose three x-values: -2, 0, and 3.
For x = -2, y = 5 - (-2) = 5 + 2 = 7.
For x = 0, y = 5 - 0 = 5.
For x = 3, y = 5 - 3 = 2.
Now, create a table with the x-values and their corresponding y-values:
| x | y |
| -2 | 7 |
| 0 | 5 |
| 3 | 2 |

Step 3: Plot the points on a graph.
Take the x-values from the table and plot them on the x-axis of the graph. Then take the corresponding y-values and plot them on the y-axis.
The three points we found are (-2, 7), (0, 5), and (3, 2).
Connect these points with a straight line.

Step 4: Solve the second equation for y in terms of x.
We have the equation: 3x - 5y = -1.
To solve for y, move the term with x to the other side of the equation and then divide both sides by -5:
-5y = -3x - 1
Dividing by -5, we have:
y = (3/5)x + 1/5

Step 5: Add the second equation to the graph.
Since the second equation is linear as well, we can represent it on the same graph. It has a slope of 3/5 and a y-intercept of 1/5.
Plot the y-intercept (0, 1/5) and then use the slope to find another point. For example, if we go up 3 units and right 5 units from the y-intercept, we get the point (5, 2).
Connect the two points with a straight line.

Step 6: Find the point of intersection.
The point where the two lines intersect represents the solution to the system of equations. In this case, it lies at approximately (2, 3).

Step 7: Check the solution.
To check if our solution is correct, substitute the x and y coordinates of the intersection point into both equations and see if they hold true.
For the first equation:
2 + 3 = 5 (True)
For the second equation:
3(2) - 5(3) = -1 (True)

Therefore, the solution to the system of equations is x = 2 and y = 3.