Question

What is the common solution for the equations y = 3x + 1 and y = x + 3? Write your answer an ordered pair!

Answer 1

(1, 4 )

Explanation:

Given the 2 equations

y = 3x + 1 → (1)

y = x + 3 → (2)

Substitute y = 3x + 1 into (2)

3x + 1 = x + 3 ( subtract x from both sides )

2x + 1 = 3 ( subtract 1 from both sides )

2x = 2 ( divide both sides by 2 )

x = 1

Substitute x = 1 into either of the 2 equations and evaluate for y

Substituting into (2)

y = 1 + 3 = 4

solution is (1, 4 )

Answer 2

(1,4)

Explanation:

Hi there!

We're given the system:

y=3x+1

y=x+3

We need to find the common solution (the point at which the lines intersect); we do this by finding the value of the variables.

Let's start with x

Since both equations equal y, we can make 3x+1 and x+3 equal to each other, because of a property known as transitivity (if a=b and b=c, then a=c)

3x+1=x+3

subtract 1 from both sides

3x=x+2

subtract x from both sides

2x=2

divide both sides by 2

x=1

we found the value of x

now we need to find the value of y

We do this by plugging x as 1 into either one of the equations to solve for y

let's use y=x+3 for example

substitute x as 1

y=1+3

add

y=4

we found the value of y.

Your question asks for the answer to be written as an ordered pair, which will be (1,4)

Hope this helps!