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Algebra 1. Help please! This is part 2

Algebra 1. Help please! This is part 2-example-1
User Kasptom
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The solution to the system of equations is x = 8/17 and y = 61/17.

By verifying the solution by substitution, 5 = 5 and -12 = -12 implying that the two equations are satisficed.

Mia's method of eliminating x by multiplying the first equation by 3 and the second equation by 2 will work

Eliminating y directly might be simpler in this case because the coefficient of y in the second equation is already -1.

The solution to Mia's system of equations is x = -1 and y = 3.

How to solve the system of equations algebraically

To solve the system of equations algebraically:

Solve the first equation for y:

3x + y = 5

y = 5 - 3x

Substitute the value of y in the second equation:

5x - 4(5 - 3x) = -12

5x - 20 + 12x = -12

17x - 20 = -12

17x = 8

x = 8 / 17

Substitute the value of x back into the first equation to find y:

3(8 / 17) + y = 5

24 / 17 + y = 5

y = 5 - 24 / 17

y = (85 - 24) / 17

y = 61 / 17

Therefore, the solution to the system of equations is x = 8/17 and y = 61/17.

To verify the solution algebraically using substitution:

Substitute the values of x and y into the original equations:

For the first equation:

3x + y = 5

3(8/17) + 61/17 = 5

24/17 + 61/17 = 5

85/17 = 5

5 = 5

For the second equation:

5x - 4y = -12

5(8/17) - 4(61/17) = -12

40/17 - 244/17 = -12

-204/17 = -12

-12 = -12

Both equations are satisfied by the values of x = 8/17 and y = 61/17.

Therefore, the solution is verified algebraically using substitution.

Mia's method of eliminating x by multiplying the first equation by 3 and the second equation by 2 will effectively eliminate x when the equations are added together.

However, eliminating y directly might be simpler in this case because the coefficient of y in the second equation is already -1, making it easier to eliminate y by adding the equations together without prior multiplication.

The original system of equations is:

2x + 3y = 7

3x - y = -6

To solve Mia system of equation

Multiply the first equation by 3, we have

6x + 9y = 21

multiply the second equation by 2, we get

6x - 2y = -12.
Now, subtract the second equation from the first equation, the x variable will be eliminated:

(6x + 9y) - (6x - 2y) = 21 - (-12)

6x + 9y - 6x + 2y = 21 + 12

11y = 33

Divide both sides of the equation by 11

y = 3.

Now, substitute this value of y back into one of the original equations. Let's use the first equation,

2x + 3y = 7:

2x + 3(3) = 7

2x + 9 = 7

2x = 7 - 9

2x = -2

x = -1

Thus, the solution to Mia's system of equations is x = -1 and y = 3.

User Tesfa Koli
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