## System of Linear EquationsThe following is a system of linear equations:\[\begin{cases}2x - 3y = 7 \\y = 3x - 7\end{cases}\]### Explanation:- **Equation 1:** \(2x - 3y = 7\) This is the first equation in the system, which represents a linear relationship between variables \(x\) and \(y\).- **Equation 2:** \(y = 3x - 7\) This is the second equation in the system. It is already solved for \(y\), showing the relationship between \(y\) and \(x\).### Solving the System:1. **Substitution Method:** Insert the expression for \(y\) from the second equation into the first equation: \[ 2x - 3(3x - 7) = 7 \] Simplify and solve for \(x\): \[ 2x - 9x + 21 = 7 \\ -7x = -14 \\ x = 2 \] Substitute \(x = 2\) back into the second equation to find \(y\): \[ y = 3(2) - 7 \\ y = 6 - 7 \\ y = -1 \] So, the solution to the system is \( x = 2 \) and \( y = -1 \).2. **Graphical Interpretation:** Each equation represents a line on a graph: - The first equation \(2x - 3y = 7 \) can be rewritten as \( y = \frac{2}{3}x - \frac{7}{3} \). - The second equation \( y = 3x - 7 \) is already in slope-intercept form \( y = mx + b \). These lines intersect at the point (2, -1), which is the solution to the system of equations.

Name: ## System of Linear EquationsThe following is a system of linear equa
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: ## System of Linear EquationsThe following is a system of linear equations:\[\begin{cases}2x - 3y = 7 \\y = 3x - 7\end{cases}\]### Explanation:- **Equation 1:** \(2x - 3y = 7\) This is the first equation in the system, which represents a linear rel