y=2-x 2. Without graphing determine whether each system has one solution , no solution, or infinitely many solutions. a) y=-5x-8 x+3y=4 e) 2x+y=4 2y=-4x+1 b) x-5y=3 2x-10y=-3 c) 3x+2y=-20 d) y=4-3x 6x+2y=8 3x+y=4 f) 6x-8=-2y g) 3x-2y=4 2x-3y=6

## Step 1: Analyze System a)### The first equation is already solved for . Substitute into the second equation: . Simplify to , which becomes . Thus, . Substitute into to get . So, the solution is , and the system has one solution.## Step 2: Analyze System b)### Multiply the first equation by 2: , which simplifies to . The second equation is . Since the left sides are the same but the right sides are different, the system has no solution.## Step 3: Analyze System c)### Multiply the second equation by -1: , which simplifies to . Add this to the first equation: . This simplifies to , so . Substitute this into the first equation: , which simplifies to . Thus, , and . The system has one solution .## Step 4: Analyze System d)### Rewrite the first equation as . This is the same as the second equation. Since both equations are the same, the system has infinitely many solutions.## Step 5: Analyze System e)### Rewrite the second equation as . Multiply the first equation by 2: , which simplifies to . Since the left sides are the same but the right sides are different, the system has no solution.## Step 6: Analyze System f)### Rewrite the first equation as . Divide by 2: . The second equation can be rewritten as . Multiply the first equation by 3: . Subtract the second equation from this: , which simplifies to , so . Substitute this into : , which means . Thus, . The system has one solution .## Step 7: Analyze System g)### This system is already in standard form. We can use any method to solve. Multiply the first equation by 3 and the second equation by -2: and . Add these equations: , so . Substitute into the first equation: , so , and . The system has one solution .