Questions: Solve the system of equations using substitution or elimination by addition. x+y=0.5 -0.5x-0.6y=-0.24 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is (Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

Solution Steps

To solve the system of equations, we can use the substitution method. First, solve the first equation for one of the variables, say \( y \). Substitute this expression for \( y \) into the second equation to find the value of \( x \). Once \( x \) is found, substitute it back into the expression for \( y \) to find the value of \( y \). This will give us the solution as an ordered pair.

From the first equation \( x + y = 0.5 \), we can express \( y \) in terms of \( x \): \[ y = 0.5 - x \]

Next, we substitute \( y \) into the second equation \( -0.5x - 0.6y = -0.24 \): \[ -0.5x - 0.6(0.5 - x) = -0.24 \]

Expanding the equation gives: \[ -0.5x - 0.3 + 0.6x = -0.24 \] Combining like terms results in: \[ 0.1x - 0.3 = -0.24 \] Adding \( 0.3 \) to both sides: \[ 0.1x = 0.06 \] Dividing by \( 0.1 \): \[ x = 0.6 \]

Now, substitute \( x = 0.6 \) back into the expression for \( y \): \[ y = 0.5 - 0.6 = -0.1 \]

Final Answer