Answer:
a.
Equation 1: y = x + 1
Equation 2: y = 4x - 5
Substitute Equation 1 into Equation 2:
x + 1 = 4x - 5
Now, solve for x:
4x - x = 1 + 5
3x = 6
x = 2
So now we have x, lets solve for y:
y = x + 1
Substitute x:
y = 2 + 1
y = 3
So the point of intersection of line y = x + 1 and line y = 4x -5 is (2,3) as shown on the graph.
Lets do the other two now:
b.
Equation 1: x + 4y = 1
Equation 2: 2x - y = -7
For this one we cannot simply substitute we have to get rid of one variable to create another equation.
Lets get rid of x for equation 3. To do this we simply times Equation 1 by 2:
Equation 3: 2x + 8y = 2
With this we can minus Equation 2 and Equation 3 to get rid of x:
2x - y = -7
-
2x + 8y = 2
-9y = -9
y = 1
Now that we have the y value, we can now find x using any equations above, lets use Equation 1:
x + 4y = 1
x + 4(1) = 1
x + 4 = 1
x = 1 - 4
x = -3
So the point of intersection is (-3,1).
c.
Equation 1: 4x + y = 11
Equation 2: y = -2x + 3
For this question, we can just do what we did for question a.
Lets substitute Equation 2 into Equation 1:
4x + (-2x + 3) = 11
4x - 2x + 3 = 11
2x + 3 = 11
2x = 11 - 3
2x = 8
x = 4
So we got our x value, let get our y value. Lets use Equation 1 for that:
4x + y = 11
4(4) + y = 11
16 + y = 11
y = 11 - 16
y = -5
So, the point of intersection is (4,-5).