A system of equations is shown below. y = -2(x - 5) 3x + y = 13 What is the value of x? — SAT

A system of equations is shown below.

y = -2(x - 5)

3x + y = 13

What is the value of $x$ ?

The value of

x

3

Substituting the expression for

y

from the first equation into the second equation gives

3x - 2(x - 5) = 13

. Distributing the

-2

yields

3x - 2x + 10 = 13

. Combining the

x

terms gives

x + 10 = 13

. Subtracting 10 from both sides of the equation yields

x = 3

Substitute the expression for

y

from the first equation into the second equation.

3x - 2(x - 5) = 13

This substitution reduces the system to a single linear equation in terms of

x

Apply the distributive property to simplify the equation.

3x - 2x + 10 = 13

Multiplying

-2

x

gives

-2x

, and multiplying

-2

-5

gives

+10

Combine like terms and isolate

x

x + 10 = 13

, which simplifies to

x = 3

Subtracting 10 from both sides gives the value of

x

Solving a system of linear equations using substitution.

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