How to find the value of x and y which satisfy both equations x-2y=24 and 8x-y=117

To find the values of x and y that satisfy both equations: x - 2y = 24 8x - y = 117 You can use the method of substitution or elimination. Let's use the elimination method: First, you can multiply the first equation by 8 to make the coefficients of y in both equations equal: 8(x - 2y) = 8(24) => 8x - 16y = 192 Now, you have the system of equations: 8x - 16y = 192 8x - y = 117 Next, subtract equation (2) from equation (1) to eliminate x: (8x - 16y) - (8x - y) = 192 - 117 This simplifies to: -15y = 75 Now, divide both sides by -15 to solve for y: y = -75 / 15 y = -5 Now that you have found the value of y, you can substitute it back into one of the original equations to solve for x. Let's use equation (1): x - 2(-5) = 24 x + 10 = 24 Subtract 10 from both sides: x = 24 - 10 x = 14 So, the values that satisfy both equations are x = 14 and y = -5.