Question

If x, minus, 4, y, equals, minus, 10x−4y=−10 and 2, x, plus, 9, y, equals, minus, 32x+9y=−3 are true equations, what would be the value of 3, x, plus, 5, y3x+5y?

Answer 1

To solve this problem, we need to solve the system of equations:

-10x - 4y = -10
-32x + 9y = -3

We can multiply the first equation by 9 and the second equation by 4 to eliminate the "y" variable:

-90x - 36y = -90
-128x + 36y = -12

Adding these two equations together, we get:

-218x = -102

Dividing both sides by -218, we get:

x = 102/218
x = 51/109

Substituting this value of x back into the second equation:

-32(51/109) + 9y = -3
-1632/109 + 9y = -3
-1632 + 981y = -327
981y = -327 + 1632
981y = 1305
y = 1305/981
y = 135/101

Now that we have the values of x and y, we can find the value of 3x + 5y:

3(51/109) + 5(135/101)
(153/109) + (675/101)
(15300/10900) + (67525/10100)
(15300 + 67525)/10900
82825/10900

So, 3x + 5y = 82825/10900.