Solve the system: 2x + 3y = 7, 3x - 5y = 1

Sure, let's solve this system of equations step by step.

Step 1: Multiply the first equation by 3 and the second equation by 2 to make the coefficients of x the same in both equations. This gives us:

6x + 9y = 21 6x - 10y = 2

Step 2: Subtract the second equation from the first to eliminate x:

(6x + 9y) - (6x - 10y) = 21 - 2 This simplifies to: 19y = 19

Step 3: Divide both sides by 19 to solve for y:

y = 19/19 = 1

Step 4: Substitute y = 1 into the first equation to solve for x:

2x + 3(1) = 7 2x + 3 = 7 2x = 7 - 3 2x = 4

Step 5: Divide both sides by 2 to solve for x:

x = 4/2 = 2

So, the solution to the system of equations is x = 2, y = 1.