Finding the point of intersection for each of the pairs of lines is doing the following:
1.) Solving for y in each of the following
2.) Setting them equal to each other, since you just found that they both equal y. Solve for x and this will give you when they intersect at which x value.
Thus, they will intersect when they are equal.
y = (-x - 3)/2 (bring 2y to the left side and x to the right and divide by 2)
y = (x+9)/4 (same method as above)
(-x - 3)/2 = (x+9)/4; solve for x.
Isolate x. Let's isolate x on the right side. Multiply the right side by 4, and thus you need to multiply the left by 4, too.
2*(-x-3) = x + 9
-2x - 6 = x + 9
Subtract 9 from right and left side and add +2x to both sides:
-15 = 3x
Divide by 3
x = -5; Thus, they intersect at x = -5; plug x = -5 into any of the equations and you will get the y value, too.
Let's pick the first equation: x=-2y-3.. so
-5 = -2y - 3;
-2 = -2y
y = 1;
Thus they intersect at (-5,1); you can also find this solution by graphing the two equations and seeing where they intersect on a graph.
For B and C, you do the exact same thing. For B I will give the answer, however, I think it is best that YOU try and do the work. If you get a conflicting answer, then show the work that you did and I can help you then. If you get the right answer, then perfect. No further explanation is needed.
B.) x = 3; y = 1, thus (3,1)
C is a little trickier:
C.) y = 2*x - 5/2
Once you have gotten both in the "y = mx + b" form, you'll notice that the slope in both of the equations is 2; thus, they will never intersect. They have different y intersects so they will not coincide either. Graph those two functions and it will be obvious why they do not ever intersect.
You're expected to know how to solve a system of equations.
Find the point of intersection of each pair of lines, if one exists.
This one suggests the Substitution Method.
. . (1) Solve one equation for one of its variables.
. . (2) Substitute this expression into the other equation.
. . (3) Solve the resulting equation for its variable.
. . (4) Solve for the other variable.
Substitute this into Equation (2): . .
And solve for
Substitute this into Equation (1): .
Therefore, the intersection is