Find the ordered pair (x, y) that satisfies both equations below: y = 3x - 2 y = x + 6 Whi… — Armed Services Vocational Aptitude Battery (ASVAB)

Find the ordered pair $(x, y)$ that satisfies both equations below:

y = 3x - 2

y = x + 6

Which of the following is the correct solution?

The correct solution is the ordered pair

(4, 10)

By setting the two expressions for y equal to each other (

3x - 2 = x + 6

), we can isolate x to find

x = 4

. Substituting

4

back into either original equation gives

y = 10

. Therefore, the solution is

(4, 10)

Set the right sides of both equations equal to each other.

3x - 2 = x + 6

Since both expressions are equal to y, they must be equal to each other.

Subtract

x

from both sides to group the variables.

2x - 2 = 6

This begins the process of isolating the variable x.

Add

2

to both sides of the equation.

2x = 8

This isolates the term with the x variable on one side and the constant on the other.

Divide both sides by

2

x = 4

This fully isolates x to find its numerical value.

Substitute

x = 4

into the second equation to find

y

y = 4 + 6 = 10

Substituting the known x value back into either original equation yields the corresponding y value.

Solving systems of linear equations using the substitution method.

Soru