\begin{aligned} 4x - 3y &= 25 \\ -2x + 5y &= -9 \end{aligned} If (x, y) is the solution to… — SAT

\begin{aligned} 4x - 3y &= 25 \\ -2x + 5y &= -9 \end{aligned}

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

Cevap: 6

To solve the system of equations, we can use the elimination method. First, multiply the second equation by 2 to align the coefficients of

x

2(-2x + 5y) = 2(-9) \implies -4x + 10y = -18

Next, add this new equation to the first equation to eliminate

x

(4x - 3y) + (-4x + 10y) = 25 + (-18)

7y = 7

y = 1

Substitute

y = 1

back into the second equation to solve for

x

-2x + 5(1) = -9

-2x + 5 = -9

-2x = -14

x = 7

Finally, calculate the value of the requested expression

x - y

x - y = 7 - 1 = 6

Thus, the correct response is 6.

Multiply the second equation by 2 to prepare for the elimination of

x

-4x + 10y = -18

This creates coefficients for

x

in both equations that are additive opposites, allowing

x

to be eliminated when the equations are added.

Add the first equation and the modified second equation together to solve for

y

7y = 7

, which simplifies to

y = 1

Adding the equations eliminates the

x

terms and leaves a single-variable equation in terms of

y

Substitute

y = 1

back into one of the original equations to solve for

x

-2x + 5(1) = -9

, which simplifies to

-2x = -14

, yielding

x = 7

Now that the value of

y

is known, it can be substituted into either equation to find the corresponding value of

x

Calculate the value of the expression

x - y

7 - 1 = 6

The question asks specifically for the value of the difference

x - y

, so we subtract the value of

y

from the value of

x

Solving systems of linear equations using the elimination method and evaluating linear combinations of the solutions.

Tahmini Süre:1m 30s

Soru