Johanna wrote the system of equations. 4 x - 3 y = 1, 5 x + 4 y = 9. If the second equation is multiplied by 4, what should the first equation be multiplied by to eliminate the x-variable by addition?

The first equation must be multiplied by -5 to eliminate x variable by addition

Step-by-step explanation:

4 x - 3 y = 1 (1)

5 x + 4 y = 9 (2)

If the second equation is multiplied by 4

5x+4y=9. ×4

We have,

20x+16y=36 (3)

The first equation should be multiplied by -5 to eliminate x variable by addition

4x-3y=1 × -5

We have

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

Add equation (3) and (4) to eliminate x variable

20x+16y=36

-20x+15y=-5

31y=31

Divide both sides by 31

y=1

Substitute y=1 into equation (1)

4 x - 3 y = 1

4x-3(1)=1

4x-3=1

4x=1+3

4x=4

Divide both sides by 4

x=1

To eliminate x

We multiply Equation 1 by -5

The results are

X = 1

Y= 1

Step-by-step explanation:

4 x - 3 y = 1. Equation 1

5 x + 4 y = 9 Equation 2

If equation 2 is multiplied by 4

4*(5x + 4y = 9)

20x + 16y = 36 Equation 3

To eliminate x

We multiply Equation 1 by -5

-5*(4 x - 3 y = 1. )

-20x +15y = -5 Equation 4

So we add Equation 3 and Equation 4

31y = 31

Y = 1

Substitute y into Equation 1

4x = 4

X = 1

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