Which description best describes the solution to the following system of equations?

y = −x + 4
y = 3x + 3

Line y = −x + 4 intersects the line y = 3x + 3.
Lines y = −x + 4 and y = 3x + 3 intersect the x-axis.
Lines y = −x + 4 and y = 3x + 3 intersect the y-axis.
Line y = −x + 4 intersects the origin.

i always get confused with these questions, please explain.

Thanks :)

clearly D is out, since it has nothing to do with the solution.

Similarly, B and C are out, because it does not matter where the lines hit the axes.

The solution is where both equations are true. Since each represents a line, that is where the lines intersect. So, (A) is the answer.

Thank you so much

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for the whole test would be nice but noo

To determine the solution to a system of equations, we need to find the values of x and y that satisfy both equations.

In this case, we have the following system of equations:

y = -x + 4 -- Equation A
y = 3x + 3 -- Equation B

There are different methods to solve these equations, such as substitution or elimination. Let's use the method of substitution to find the intersection point(s) of these two lines.

1. Start by equating the two equations:
-x + 4 = 3x + 3

2. Solve the equation for x:
4 = 4x + 3

Subtract 3 from both sides:
1 = 4x

Divide both sides by 4:
x = 1/4

3. Substitute the value of x back into one of the original equations to find y:
y = 3(1/4) + 3

Multiply 3 by 1/4:
y = 3/4 + 3

Convert 3 to a fraction with a common denominator:
y = 3/4 + 12/4

Add the fractions:
y = 15/4

Therefore, the solution to the system of equations is x = 1/4 and y = 15/4.

Now, let's analyze the answer choices:

1. Line y = -x + 4 intersects the line y = 3x + 3.
This statement is correct since we found the point of intersection.

2. Lines y = -x + 4 and y = 3x + 3 intersect the x-axis.
To check if this statement is correct, we substitute y = 0 into the equations and solve for x.
When y = 0, the first equation becomes:
0 = -x + 4

Solve for x:
x = 4

When y = 0, the second equation becomes:
0 = 3x + 3

Solve for x:
x = -1

Therefore, only one of the lines intersects the x-axis, so this statement is incorrect.

3. Lines y = -x + 4 and y = 3x + 3 intersect the y-axis.
To check if this statement is correct, we substitute x = 0 into the equations and solve for y.
When x = 0, the first equation becomes:
y = 4

When x = 0, the second equation becomes:
y = 3

Therefore, both lines intersect the y-axis, so this statement is correct.

4. Line y = -x + 4 intersects the origin.
To check if this statement is correct, we substitute x = 0 and y = 0 into the equation:
0 = -0 + 4
0 = 4

This is not true, so the statement is incorrect. The line does not pass through the origin.

Therefore, the correct description is:
- Line y = -x + 4 intersects the line y = 3x + 3.
- Lines y = -x + 4 and y = 3x + 3 intersect the y-axis.