solve the linear equation,
y=4x and y+x=5 tell how you got the answer.
A.)(-4,1)
B.)(1,4)
C.)(-3,2)
D.)(2,3)
y = 4x
y + x = 5
Use substitution
4x + x = 5
5x = 5
x = 1
Substitute again
y + x = 5
y + 1 = 5
y = 4
The answer is B: (1,4)
Well, these equations have got a bit of a comedy duo thing going on. Let's see if we can unpack their punchline!
First, we have y = 4x. Since y and x are both in terms of each other, that means we can substitute this expression for y in the second equation.
So, instead of y + x = 5, we can now write 4x + x = 5.
Adding the x terms together, we get 5x = 5.
Now, to find x, we divide both sides by 5. That leads us to x = 1.
Substitute this value of x back into the first equation, y = 4x, and we find that y = 4 * 1, or y = 4.
So the solution to these equations is (1, 4), which, coincidentally, is option B. And that's how this comedy duo managed to solve their linear equation conundrum!
To solve the linear equation system, we will use the method of substitution.
Given equations:
1. y = 4x
2. y + x = 5
We can substitute the value of y from equation 1 into equation 2, since both equations are equal to y:
4x + x = 5
Now, combine like terms:
5x = 5
Dividing both sides by 5, we get:
x = 1
To find the corresponding value of y, substitute the value of x back into equation 1:
y = 4(1)
y = 4
Therefore, the solution to the linear equation system is x = 1 and y = 4, which corresponds to option B, (1, 4).
To solve the linear equation y = 4x and y + x = 5, we can use the substitution method or the elimination method.
Let's start with the substitution method:
Step 1: Rearrange the second equation to solve for y:
y + x = 5
y = 5 - x
Step 2: Substitute the value of y from the second equation into the first equation:
4x = 5 - x
Step 3: Now, solve for x:
4x + x = 5
5x = 5
x = 1
Step 4: Substitute the value of x back into either equation to solve for y. We'll use the second equation:
y + 1 = 5
y = 5 - 1
y = 4
Therefore, the solution to the linear equations y = 4x and y + x = 5 is (1, 4).
The correct answer is B.)(1,4).