What is the solution to this system of equations?

Question image

Understand the Problem

The question is asking for the solution to a system of equations. It requires solving for the values of x and y that satisfy both equations given in the image.

Answer

The solution is $(-2, 3)$.
Answer for screen readers

The solution to the system of equations is $(-2, 3)$.

Steps to Solve

  1. Identify the equations
    The system of equations is:

    • Equation 1: $-3x + 5y = 21$
    • Equation 2: $6x - y = -15$
  2. Solve for one variable
    Let's solve Equation 2 for $y$.
    Rearranging gives us: $$ y = 6x + 15 $$

  3. Substitute into the first equation
    Now substitute the expression for $y$ from Equation 2 into Equation 1:
    $$ -3x + 5(6x + 15) = 21 $$

  4. Simplify and solve for $x$
    Expanding this gives: $$ -3x + 30x + 75 = 21 $$ Combine like terms: $$ 27x + 75 = 21 $$ Now isolate $x$: $$ 27x = 21 - 75 $$ $$ 27x = -54 $$ $$ x = -2 $$

  5. Find $y$ using the value of $x$
    Substitute $x = -2$ back into the expression for $y$:
    $$ y = 6(-2) + 15 $$ $$ y = -12 + 15 $$ $$ y = 3 $$

  6. Solution pairs
    The solution to the system of equations is: $$ (x, y) = (-2, 3) $$

The solution to the system of equations is $(-2, 3)$.

More Information

The solution $(-2, 3)$ satisfies both given equations, meaning both equations hold true when these values are substituted back in.

Tips

  • Not isolating one variable correctly can lead to errors. Always double-check simplifications.
  • Forgetting to substitute the variable back into one of the original equations to find the second variable.
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