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How do you solve this system of equations??
3x-y=17
-2x-3y = -4

User AlanSTACK
by
7.3k points

2 Answers

3 votes

Answer:

3x-y=17

-2x-3y=-4

per combination:

-3(3x-y)=17)

-9x+3y=-51

-9x+3y=-51

-2x-3y=-4

-11x=-55

x=5

we calculate the value of y:

3x-y=17

15-y=17

-y=17-15

y= -2

solution (5,-2)

verification :

-2x-3y=-4

-10+6=-4

User Quinekxi
by
7.8k points
1 vote

answer:

To solve the system of equations:

3x - y = 17

-2x - 3y = -4

We can use the method of substitution or elimination.

Method 1: Substitution

Step 1: Solve one equation for one variable in terms of the other variable.

From the first equation, solve for y:

y = 3x - 17

Step 2: Substitute the expression for y into the other equation.

Replace y in the second equation with 3x - 17:

-2x - 3(3x - 17) = -4

Step 3: Simplify and solve for x.

-2x - 9x + 51 = -4

-11x + 51 = -4

-11x = -4 - 51

-11x = -55

x = -55 / -11

x = 5

Step 4: Substitute the value of x back into either equation to solve for y.

Using the first equation:

3(5) - y = 17

15 - y = 17

-y = 17 - 15

-y = 2

y = -2

So, the solution to the system of equations is x = 5 and y = -2.

Method 2: Elimination

Step 1: Multiply the equations by appropriate constants to make the coefficients of one variable opposite in sign.

Multiply the first equation by 3 and the second equation by -1:

9x - 3y = 51

2x + 3y = 4

Step 2: Add the equations together to eliminate one variable.

(9x - 3y) + (2x + 3y) = 51 + 4

11x = 55

x = 55 / 11

x = 5

Step 3: Substitute the value of x back into either equation to solve for y.

Using the first equation:

3(5) - y = 17

15 - y = 17

-y = 17 - 15

-y = 2

y = -2

So, the solution to the system of equations is x = 5 and y = -2.

Both methods give the same solution: x = 5 and y = -2.

~~Alli~~

User Pschill
by
9.0k points

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