Question

solve the systems of equations by any convenient method, if a solution exists.\

$$\begin{cases}2x = 7y - 9\\\\9x = 63 - 3y\\end{cases}$$

\what is the solution to the system of equations? select the correct answer below and, if necessary, fill in any answer boxes to co\\(\boldsymbol{\circ}\\) a. the solution is \\(x = \square\\), \\(y = \square\\). (type integers or simplified fractions.)\\(\boldsymbol{\circ}\\) b. the system of equations has infinitely many solutions.\\(\boldsymbol{\circ}\\) c. the system of equations has no solution.

Explanation:

Step1: Rewrite equations to standard form

Equation1: $2x - 7y = -9$
Equation2: $9x + 3y = 63$
Simplify Equation2: divide by 3: $3x + y = 21$

Step2: Isolate y from Equation2

$y = 21 - 3x$

Step3: Substitute y into Equation1

$2x - 7(21 - 3x) = -9$

Step4: Expand and solve for x

$2x - 147 + 21x = -9$
$23x = 138$
$x = \frac{138}{23} = 6$

Step5: Substitute x=6 into y's expression

$y = 21 - 3(6) = 21 - 18 = 3$

Answer:

A. The solution is x = 6, y = 3.