7. x=3y-1 and 2x-6y=-2 3. ) 4x-7y=7 12x-21y=24

Let's solve each system of equations one by one.### Problem 7:We have the following system of equations:1. 2. **Step 1: Substitute Equation 1 into Equation 2**Since , substitute this expression for in Equation 2: **Step 2: Simplify and Solve for ** This simplifies to: This equation is always true, which means that the two equations are dependent and represent the same line. Therefore, there are infinitely many solutions along the line described by .### Problem 8:We have the following system of equations:1. 2. **Step 1: Simplify Equation 2**Notice that Equation 2 can be simplified by dividing all terms by 3: This simplifies to: **Step 2: Compare with Equation 1**Now we have:1. 2. These two equations are inconsistent because they imply that the same linear combination of and equals two different numbers (7 and 8). Therefore, there is no solution to this system; the lines are parallel and do not intersect.In summary:- For Problem 7, there are infinitely many solutions.- For Problem 8, there is no solution.