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4x-5y=-19; -x-2y=8 solve using elimination and multiplication

User Tamekia
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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.

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