Answer:
Explanation:
o solve the system of equations -5x+4y=-7 and 17x-16y=31, we can use the method of elimination.
First, we need to multiply the first equation by 4, and the second equation by 5, so that the coefficient of y is the same in both equations. This gives us:
-20x + 16y = -28 (multiplying the first equation by 4)
85x - 80y = 155 (multiplying the second equation by 5)
Now we can add the two equations together to eliminate y:
-20x + 16y = -28
85x - 80y = 155
65x - 64y = 127
Next, we can solve for x by dividing both sides of the equation by 65:
65x - 64y = 127
x = (127 + 64y) / 65
Now we can substitute this expression for x into either of the original equations to solve for y. Let's use the first equation:
-5x + 4y = -7
-5((127 + 64y) / 65) + 4y = -7
-635/65 - 256y/65 + 260y/65 = -7
4y/65 = -98/65
y = -24.5
Finally, we can substitute this value of y back into either of the expressions we found for x. Using the expression we found earlier:
x = (127 + 64y) / 65
x = (127 + 64(-24.5)) / 65
x = -0.5
Therefore, the solution to the system of equations -5x+4y=-7 and 17x-16y=31 is x = -0.5 and y = -24.5.