How do you solve the system 2x + y = 5 and 3x – y = 10?

To solve the system 2x + y = 5 and 3x - y = 10, you can use either the method of substitution or elimination. Method of Substitution: Step 1: Solve one of the equations for one of the variables. For example, solve the first equation for y: y = 5 - 2x Step 2: Substitute this expression for y into the second equation and solve for x: 3x - (5 - 2x) = 10 Simplify by distributing the negative: 3x - 5 + 2x = 10 Combine like terms: 5x - 5 = 10 Add 5 to both sides: 5x = 15 Divide both sides by 5: x = 3 Step 3: Substitute this value for x into one of the original equations and solve for y: 2(3) + y = 5 6 + y = 5 Subtract 6 from both sides: y = -1 Therefore, the solution to the system 2x + y = 5 and 3x - y = 10 is x = 3 and y = -1. Method of Elimination: Step 1: Add the two equations together to eliminate y: 2x + y + 3x - y = 5 + 10 Simplify by combining like terms: 5x = 15 Divide both sides by 5: x = 3 Step 2: Substitute this value for x into one of the original equations and solve for y: 2(3) + y = 5 6 + y = 5 Subtract 6 from both sides: y = -1 Therefore, the solution to the system 2x + y = 5 and 3x - y = 10 is x = 3 and y = -1, which is the same as the solution found using the method of substitution.