Question

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

$$\begin{cases}3x = 7y - 9\\\\5x = 29 - 3y\\end{cases}$$

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

Explanation:

Step1: Rewrite in standard form

Rearrange equations to $ax+by=c$:
$3x - 7y = -9$
$5x + 3y = 29$

Step2: Eliminate one variable

Multiply first eq by 3, second by 7:
$9x - 21y = -27$
$35x + 21y = 203$
Add the two equations:
$9x + 35x -21y +21y = -27 + 203$
$44x = 176$

Step3: Solve for $x$

Isolate $x$ by dividing:
$x = \frac{176}{44} = 4$

Step4: Substitute $x=4$ to find $y$

Use $3x = 7y -9$:
$3(4) = 7y -9$
$12 = 7y -9$
$7y = 12 + 9 = 21$
$y = \frac{21}{7} = 3$

Answer:

A. The solution is $x = 4$, $y = 3$. (Type integers or simplified fractions.)