Question

4x+3y=-1
5x+4y=1 solve by elimination

Answer 1

x = -7; y = 9

Step-by-step explanation:

We can start by multiplying the first equation by 5 and the second equation by -4.

This will allow us to eliminate x since 20x - 20x = 0:

Multiplying 4x + 3y = -1 by 5:

5(4x + 3y = -1)

20x + 15y = -5

Multiplying 5x + 4y = 1 by -4:

-4(5x + 4y = 1)

-20x - 16y = -4

Solving for y:

Now, we add the two equations to eliminate x and solve for y:

20x + 15y = -5

+

-20x - 16y = - 4

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(20x - 20x) + (15y - 16y) = (-5 - 4)

(-y = -9) / -1

Thus, y = 9.

Solving for x:

Now, we can solve for x by plugging in 9 for y in 4x + 3y = -1:

4x + 3(9) = -1

(4x + 27 = -1) - 27

(4x = -28) / 4

x = -7

Thus, x = -7.

Answer 2

To solve the system of equations using elimination, multiply one equation by a constant to eliminate a variable, then solve for the remaining variable. The solution to the given system of equations is x = -7 and y = 9.

Step-by-step explanation:

To solve the system of equations using elimination, we need to eliminate one of the variables by multiplying one of the equations by a constant. In this case, we can eliminate the x variable by multiplying the first equation by 5 and the second equation by 4, which will give us:

20x + 15y = -5

20x + 16y = 4

Now subtract the first equation from the second equation to eliminate the x variable: 20x + 16y - (20x + 15y) = 4 - (-5)

This simplifies to: y = 9

Substitute the value of y back into one of the original equations to find the value of x:

4x + 3(9) = -1

4x + 27 = -1

4x = -28

x = -7

Therefore, the solution to the system of equations is x = -7 and y = 9.