Answer:
(2,7)
Step-by-step explanation:
Since the two equations are both set equal to y. I would use substitution.
y = 8x-9
y = 4x-1
Substitute the second equation in for y into the first equation
4x-1 = 8x-9
Subtract 4x from each side
4x-4x-1 = 8x-4x-9
-1 = 4x-9
Add 9 to each side
-1 +9 = 4x-9+9
8 =4x
Divide each side by 4
8/4 =4x/4
2 =x
But we still need to find y
y =4x-1
y = 4(2) -1
y = 8-1
y =7
The solution is (2,7)
When we graph the two lines, the will cross at (2,7) which is the solution to the system of equations
Answer:
Part A: I solved using substitution. I found the solution to be (2,7).
Part B: The two equations when graph will intersect at (2,7). The reason we already know this before graphing is because we did the algebra in the previous question. I replaced the 2nd y with what the first y (which was 8x-9 equaled). I was finding when the y's are the same for both lines by doing this. I then found that the y's were the same when x=2. After finding that the y's would be the same at x=2 which was at y=7, this told me the lines would cross at (2,7).
We can even check to see if this point will be on both lines by plugging this into both equations and see if each is true. If both are true and both have to be true, then system will cross at (2,7).
Let's check:
y=8x-9 with (2,7)
7=8(2)-9
7=16-9
7=7 This is a true equation so (2,7) is on this line y=8x-9.
y=4x-1 with (2,7)
7=4(2)-1
7=8-1
7=7 This is a true equation so (2,7) is on this line y=4x-1.
If both lines have the point (2,7) on it, then they will cross at that point.
Step-by-step explanation:
Part A:
The system is:
y=8x-9
y=4x-1
I prefer to use substitution since y is solved for in at least one of the equations.
Since y=8x-9 and y=4x-1, then 8x-9=4x-1 by transitive property.
Or I just substituted y in the second equation with the y (which is 8x-9) from the first equation.
So now we need to solve:
8x-9=4x-1
Subtract 4x on both sides:
4x-9=-1
Add 9 on both sides:
4x=8
Divide both sides by 4:
x=8/4
Simplify the fraction on the right hand side:
x=2
So the intersection is at x=2.
We need to find the y that corresponds to x=2.
You may use either equation that they gave you.
Both will produce the same y.
We can check it and see, and plug into both.
y=8x-9 with x=2
y=8(2)-9
y=16-9
y=7
y=4x-1 when x=2
y=4(2)-1
y=8-1
y=7
They both should have gave the same answer since we were finding when they had the same x and same y which is at (x,y)=(2,7).
Part B:
Graphing the equations should show us the solution to the system. The solution is the point or points they have in common. It will be the intersection of the lines if they cross. Ours do cross, and they cross at (2,7).
The algebra we did above proves this.
We found when the y's were the same by substituting one equation's y for the other. We then solve this equation for x. This x, again told us when the y's were going to be the same. It also told us for what x's those y's would be the same.
I did a verification in the answer part of this explanation.
