Systems of 2 linear equations in 2 variables：练习题

Consider the system of equations below:
\(2x + 3y = 12\)
\(y = 4 - \frac{2}{3}x\)
How many solutions \((x, y)\) does this system of equations have?

In the system of equations below, \( c \) is a constant. If the system has no solution, what is the value of \( c \)?
\( 5x - 2y = 10 \)
\( cx + 6y = 15 \)

What is the value of \( x \) in the solution to the system of equations below?
\( \frac{1}{2}x - \frac{1}{3}y = 5 \)
\( \frac{1}{4}x + \frac{2}{3}y = 10 \)

If \( y = 2x - 3 \) and \( x + y = 12 \), what is the value of \( x \)?

Consider the system of equations below:
\(3x + 2y = 16\)
\(x - y = 2\)
What is the value of \(y\) in the solution to this system?

If the system of linear equations \( 3x - 5y = 12 \) and \( kx + 10y = -24 \) has infinitely many solutions, what is the value of the constant \( k \)?

In the system of equations below, \( c \) and \( d \) are constants. If the system has infinitely many solutions, what is the value of \( \frac{d}{c} \)?
\( 4x + cy = 10 \)
\( 12x + 9y = d \)

In the system of equations below, what is the value of \( x + y \)?
\( 2x + 3y = 11 \)
\( 3x + 2y = 9 \)