The variables x and y satisfy the system of equations below. y = 10 - 2x 3x - y = 5 What i… — SAT

The variables $x$ and $y$ satisfy the system of equations below.

y = 10 - 2x

3x - y = 5

What is the value of $x$ ?

Substituting the expression for

y

from the first equation,

10 - 2x

, into the second equation yields

3x - (10 - 2x) = 5

. Distributing the negative sign results in

3x - 10 + 2x = 5

. Combining the like terms of

x

gives

5x - 10 = 5

. Adding 10 to both sides of the equation results in

5x = 15

. Finally, dividing both sides by 5 gives

x = 3

Substitute the expression for

y

from the first equation into the second equation.

3x - (10 - 2x) = 5

To eliminate the variable

y

and obtain a single linear equation in terms of

x

Distribute the negative sign through the parentheses and combine like terms.

3x - 10 + 2x = 5

, which simplifies to

5x - 10 = 5

To simplify the linear equation before isolating the variable.

Isolate the variable

x

by adding 10 to both sides and then dividing by 5.

5x = 15

, which gives

x = 3

To determine the value of

x

Solving systems of linear equations using substitution

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