Final answer:
The solution to the system of equations 4x-5y=-19 and -x-2y=8 using elimination and multiplication is x = -6 and y = -1. We multiplied the second equation by 4 and then added it to the first equation to eliminate x and solve for y. Finally, we substituted y = -1 into one of the original equations to find x.
Step-by-step explanation:
To solve the system of equations 4x-5y=-19 and -x-2y=8 using elimination and multiplication, we need to manipulate the equations such that one variable will cancel out when we add or subtract them. First, multiply the second equation by 4 to line up with the coefficient of x in the first equation:
Original second equation: -x - 2y = 8
Multiply by 4: -4x - 8y = 32
Now we have:
1st equation: 4x - 5y = -19
Modified 2nd equation: -4x - 8y = 32
Adding both equations together to eliminate x:
4x - 5y + (-4x - 8y) = -19 + 32
0x - 13y = 13
Divide both sides by -13 to solve for y:
y = 13 / -13
y = -1
Substitute y = -1 into one of the original equations to solve for x. We'll use the first equation:
4x - 5(-1) = -19
4x + 5 = -19
4x = -24
Divide both sides by 4:
x = -24 / 4
x = -6
The solution for the system of equations is x = -6 and y = -1.