I have major issues with problems like these,please I need help.

For these systems of linear equations in questions
-Determine how many solutions exist
-Use either elimination or substitution to find the solutions (if any)
1. y = 2x + 3 and y = -x - 4

2. 2x + 3y = 8 and 3x + 2y = 7

3. x + y = 3 and y = x + 3

as long as the slopes are different, there will be exactly one solution. That is true for all three of these pairs, with solutions

(-7/3,-5/3)
(1,2)
(0,3)

Sure! I'd be happy to help you with these linear equations problems. Let's go through each question step by step.

1. y = 2x + 3 and y = -x - 4

To determine how many solutions exist for this system of equations, we need to compare the slopes of the two equations. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope. In the first equation, the slope is 2, and in the second equation, the slope is -1.

Since the slopes are not equal, these two lines are not parallel. Therefore, there is exactly one solution for this system of equations. To find the solution, we can use either elimination or substitution.

Since both equations are already solved for y, we can set them equal to each other:

2x + 3 = -x - 4

To solve for x, we can add x to both sides of the equation:

2x + x + 3 = -x + x - 4

This simplifies to:

3x + 3 = -4

Next, we can subtract 3 from both sides:

3x + 3 - 3 = -4 - 3

This simplifies to:

3x = -7

Finally, we can divide both sides by 3 to solve for x:

x = -7/3

Substituting the value of x back into either of the original equations, we can solve for y:

y = 2(-7/3) + 3

Simplifying this gives us:

y = -14/3 + 3

y = -14/3 + 9/3

y = -5/3

Therefore, the solution to this system of equations is (x, y) = (-7/3, -5/3).

2. 2x + 3y = 8 and 3x + 2y = 7

To determine how many solutions exist for this system of equations, we can again compare the slopes of the two equations. In this case, one equation has a slope of -2/3, while the other has a slope of -3/2.

Similar to the previous question, since the slopes are not equal, these lines are not parallel. Therefore, there is exactly one solution for this system of equations. We can proceed to solve it using either elimination or substitution.

Let's use the substitution method to solve this system of equations. We can solve the first equation for x:

2x + 3y = 8
2x = 8 - 3y
x = (8 - 3y)/2

Now we can substitute this expression for x into the second equation:

3(8 - 3y)/2 + 2y = 7

Simplifying this equation gives us:

24 - 9y + 4y = 14
-5y = -10
y = 2

Substituting the value of y back into the first equation, we can solve for x:

2x + 3(2) = 8
2x + 6 = 8
2x = 2
x = 1

Therefore, the solution to this system of equations is (x, y) = (1, 2).

3. x + y = 3 and y = x + 3

To determine how many solutions exist for this system of equations, we can see that the second equation is already solved for y. We can substitute this expression for y in the first equation:

x + (x + 3) = 3

Simplifying this equation gives us:

2x + 3 = 3
2x = 0
x = 0

Substituting the value of x back into either of the original equations, we can solve for y:

y = 0 + 3
y = 3

Therefore, the solution to this system of equations is (x, y) = (0, 3).

I hope this helps! Let me know if there's anything else I can assist you with.