y = 4x + 1\n4y = 15x - 8\nthe solution to the given system of equations is (x, y). what is the value of x - y?

Explanation:

Step1: Substitute y in the second - equation

Since (y = 4x + 1), substitute it into (4y=15x - 8). We get (4(4x + 1)=15x - 8).

Step2: Expand the left - hand side

Expand (4(4x + 1)) to (16x+4). So the equation becomes (16x + 4=15x - 8).

Step3: Solve for x

Subtract (15x) from both sides: (16x-15x+4=15x - 15x-8), which simplifies to (x+4=-8). Then subtract 4 from both sides: (x=-8 - 4=-12).

Step4: Find the value of y

Substitute (x = - 12) into (y = 4x + 1), so (y=4\times(-12)+1=-48 + 1=-47).

Step5: Calculate x - y

(x - y=-12-(-47)=-12 + 47 = 35).

Answer:

35