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3x-5y=9
-4x+2y=2
Solve using algebraic methods.

User Shankze
by
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2 Answers

5 votes

Answer:

3x-5y=9

-4x+2y=2

by combination

2(3x-5y=9)

5(-4x+2y=2)

6x-10y=18

-20x+10y=10

-14x=28

x=-2

we calculate y:

3x-5y=9

-6-5y=9

-5y=9+6

y=-3

solutions: (-2;-3)

Explanation:

User Bo Buchanan
by
8.5k points
4 votes

Answer:

the solution to the system of equations is:

x = -32

y = -21

Explanation:

To solve the system of equations using algebraic methods, you can use the method of either substitution or elimination. In this example, I'll use the elimination method to solve for x and y. Here are the equations:

3x - 5y = 9

-4x + 2y = 2

We can start by manipulating the equations so that when added or subtracted, one of the variables cancels out. Let's start by multiplying both sides of the second equation by 5 to make the coefficients of y in both equations cancel out:

3x - 5y = 9

(-4x + 2y) * 5 = 2 * 5

This gives us:

3x - 5y = 9

-20x + 10y = 10

Now, we can add these two equations to eliminate the variable y:

(3x - 5y) + (-20x + 10y) = 9 + 10

Now, simplify:

(3x - 20x) + (-5y + 10y) = 19

-17x + 5y = 19

Now, we have a new equation:

-17x + 5y = 19

Now, we have a system of two equations with two variables:

3x - 5y = 9

-17x + 5y = 19

Next, you can either use the elimination or substitution method to solve for x and y. Let's use the elimination method again to eliminate y:

Multiply the first equation by 5 to make the coefficients of y in both equations cancel out:

5(3x - 5y) = 5(9)

This gives us:

5(3x) - 5(5y) = 45

15x - 25y = 45

Now, add this equation to the fourth equation:

(15x - 25y) + (-17x + 5y) = 45 + 19

Now, simplify:

(15x - 17x) + (-25y + 5y) = 64

-2x = 64

Now, divide both sides by -2 to solve for x:

-2x / -2 = 64 / -2

x = -32

Now that we have found the value of x, you can substitute it back into one of the original equations to solve for y. Using the first equation:

3x - 5y = 9

3(-32) - 5y = 9

-96 - 5y = 9

Now, add 96 to both sides:

-5y = 9 + 96

-5y = 105

Finally, divide both sides by -5 to solve for y:

-5y / -5 = 105 / -5

y = -21

User Geofftnz
by
7.5k points

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