Consider the system of equations below. x = 2y 3x - y = 10 If (x, y) is the solution to th… — SAT

Consider the system of equations below.

x = 2y

3x - y = 10

If $(x, y)$ is the solution to the system of equations above, what is the value of $x$ ?

Answer: 4

The value of

x

4

The system of equations can be solved by substituting

x = 2y

from the first equation into the second equation, which gives

3(2y) - y = 10

. Simplifying this equation yields

6y - y = 10

, or

5y = 10

. Dividing by

5

gives

y = 2

. Substituting

y = 2

back into the first equation yields

x = 2(2) = 4

. Therefore, the value of

x

4

Substitute the expression for

x

from the first equation into the second equation.

3(2y) - y = 10

Since the first equation gives

x

in terms of

y

, substituting it into the second equation reduces the system to a single linear equation in one variable.

Solve the resulting equation for

y

y = 2

Simplifying

3(2y) - y = 10

yields

6y - y = 10

, which simplifies further to

5y = 10

. Dividing both sides by

5

gives

y = 2

Substitute the value of

y

back into the first equation to solve for

x

x = 4

Using

x = 2y

and substituting

y = 2

gives

x = 2(2) = 4

Solving systems of linear equations using the substitution method.

Question