If (x, y) is the solution to the system of equations below, what is the value of x? y = 2x… — SAT

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

y = 2x + 1

3x + 2y = 16

Answer: 2

The correct answer is 2.

Substituting

y = 2x + 1

into the second equation yields

3x + 2(2x + 1) = 16

. Expanding this expression gives

3x + 4x + 2 = 16

, which simplifies to

7x + 2 = 16

. Subtracting 2 from both sides gives

7x = 14

, and dividing by 7 yields

x = 2

Substitute the expression for

y

from the first equation into the second equation.

3x + 2(2x + 1) = 16

This reduces the system of two variables to a single equation in terms of

x

Expand and simplify the equation by distributing and combining like terms.

7x + 2 = 16

Simplifying the equation makes it easier to isolate the variable

x

Isolate the variable

x

by performing inverse operations.

x = 2

Subtracting 2 and then dividing by 7 isolates

x

to find its value.

Solving a system of linear equations using the substitution method.

Alternatively, you can multiply the first equation by 2 to get

-4x + 2y = 2

and subtract it from

3x + 2y = 16

to eliminate

y

, which also yields

7x = 14

and thus

x = 2

Estimated Time:1m 0s

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