A system of two linear equations is given below. y = x - 2 2x - 3y = 1 If (x, y) is the so… — SAT

A system of two linear equations is given below.

y = x - 2

2x - 3y = 1

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

The value of

x

is 5.

To find the value of

x

, substitute the expression for

y

from the first equation into the second equation:

2x - 3(x - 2) = 1

. Distribute the

-3

to obtain

2x - 3x + 6 = 1

, which simplifies to

-x + 6 = 1

. Subtracting 6 from both sides gives

-x = -5

. Multiplying or dividing both sides by

-1

yields

x = 5

Substitute the expression for

y

from the first equation into the second equation.

2x - 3(x - 2) = 1

Substituting the expression reduces the system of two equations to one linear equation containing only the variable

x

Distribute the coefficient

-3

to both terms inside the parentheses.

2x - 3x + 6 = 1

Applying the distributive property removes the parentheses so that like terms can be combined.

Combine like terms and isolate

x

-x + 6 = 1 \implies -x = -5 \implies x = 5

Combining the

x

terms and subtracting 6 from both sides isolates

-x

, allowing you to find the final value of

x

Solving systems of linear equations using the substitution method

Alternatively, you can solve this system using elimination. First, rewrite the first equation in standard form by subtracting

x

from both sides, which gives

-x + y = -2

. Next, multiply this equation by 3 to align coefficients:

-3x + 3y = -6

. Adding this result directly to the second equation,

2x - 3y = 1

, eliminates the

y

terms and leaves

-x = -5

, which simplifies to

x = 5

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