Two linear equations are defined as follows: 3x + 2y = 12 x - 2y = 4 If the ordered pair (… — SAT

Two linear equations are defined as follows:

3x + 2y = 12

x - 2y = 4

If the ordered pair $(x, y)$ satisfies both equations, what is the value of $x$ ?

Answer: 4

The value of

x

is 4.

Adding the two equations

3x + 2y = 12

and

x - 2y = 4

eliminates the

y

terms, resulting in

4x = 16

. Dividing both sides by 4 gives the value of

x

as 4.

Add the two equations together to eliminate the

y

variable.

4x = 16

Since the coefficients of

y

are opposites (

2

and

-2

), adding the equations eliminates

y

directly.

Divide both sides of the equation by 4.

x = 4

To isolate the variable

x

Solving systems of linear equations using the elimination method.

We can solve the second equation for

x

to get

x = 2y + 4

. Substituting this expression into the first equation gives

3(2y + 4) + 2y = 12

, which simplifies to

6y + 12 + 2y = 12

, or

8y = 0

, meaning

y = 0

. Substituting

y = 0

back into

x = 2y + 4

yields

x = 4

Estimated Time:45s

Question