Questions: QUESTION 5 If possible, solve the system of equations. Use any method. If there is not a unique solution to a system, say why. 7x = 7 - 7y -4x + 3y = 45

Transcript text: QUESTION 5 If possible, solve the system of equations. Use any method. If there is not a unique solution to a system, say why. \[ \begin{array}{l} 7 x=7-7 y \\ -4 x+3 y=45 \end{array} \]

Solution

Solution Steps

To solve the system of equations, we can use the substitution method. First, solve the first equation for \( x \) in terms of \( y \). Then, substitute this expression into the second equation to find the value of \( y \). Finally, use the value of \( y \) to find \( x \).

Step 1: Solve the First Equation for \( x \)

Starting with the first equation: \[ 7x = 7 - 7y \] we can isolate \( x \): \[ x = 1 - y \]

Step 2: Substitute \( x \) into the Second Equation

Next, we substitute \( x = 1 - y \) into the second equation: \[ -4(1 - y) + 3y = 45 \] This simplifies to: \[ -4 + 4y + 3y = 45 \] Combining like terms gives: \[ 7y - 4 = 45 \]

Step 3: Solve for \( y \)

Now, we solve for \( y \): \[ 7y = 45 + 4 \] \[ 7y = 49 \] \[ y = 7 \]

Step 4: Substitute \( y \) Back to Find \( x \)

Using the value of \( y \) in the expression for \( x \): \[ x = 1 - y = 1 - 7 = -6 \]