Understand the Problem
The question appears to ask about the transcription of the image, which likely contains mathematical content or concepts that need to be processed or interpreted.
Answer
The solution is $x = \frac{12}{17}$ and $y = \frac{42}{17}$.
Answer for screen readers
The solution to the system of equations is: $$ x = \frac{12}{17}, \quad y = \frac{42}{17} $$
Steps to Solve
- Write down the equations
The given equations are: $$ 3x + 4y = 12 \quad (1) $$ $$ 2x - 3y = -6 \quad (2) $$
- Solve one equation for one variable
Let's solve equation (1) for $x$: $$ 3x = 12 - 4y \ x = \frac{12 - 4y}{3} \quad (3) $$
- Substitute into the other equation
Substitute equation (3) into equation (2): $$ 2\left(\frac{12 - 4y}{3}\right) - 3y = -6 $$ Multiply through by 3 to eliminate the fraction: $$ 2(12 - 4y) - 9y = -18 $$
- Simplify and solve for $y$
Distributing and combining like terms: $$ 24 - 8y - 9y = -18 \ 24 - 17y = -18 \ -17y = -18 - 24 \ -17y = -42 \ y = \frac{-42}{-17} = \frac{42}{17} \quad (4) $$
- Substitute back to find $x$
Now substitute $y$ from equation (4) back into equation (3): $$ x = \frac{12 - 4\left(\frac{42}{17}\right)}{3} \ = \frac{12 - \frac{168}{17}}{3} \ = \frac{\frac{204 - 168}{17}}{3} \ = \frac{\frac{36}{17}}{3} \ = \frac{36}{51} = \frac{12}{17} \quad (5) $$
The solution to the system of equations is: $$ x = \frac{12}{17}, \quad y = \frac{42}{17} $$
More Information
This solution represents the point of intersection of the two lines described by the given linear equations. Each variable represents a dimension in the two-dimensional coordinate system and this pair can be plotted on a graph.
Tips
- Forgetting to distribute properly when substituting values into another equation.
- Misplacing negative signs which can lead to incorrect values for $x$ or $y$.
- Failing to reduce fractions to their simplest form.
