Question

Solve the system of two equations using substitution
y=2+3x
4x-3y=-16
Answer
No give two numbers like this
(Number,Number)
Answer
Solve the system of equations
2x+6y=-18
X=5y-x
Answer: (__,__)
Answer
Solve the system of two liner equations
-3x-4y=-23
3x-5y=5
Answer
No give an answer like (number,number)
Answer
How many solutions
8x-6y=48
8x+6y=48
Answer
4x-6y=-48
-2x+4y=30
Give answer as (#,#)
Answer
Solve the system of equations
3x-4y=40
5x-5y=55
Answered by GPT 3.5
To solve the system of equations using substitution, we can solve one equation for one variable and substitute it into the other equation.

In this case, let's solve the first equation for y:

y = 2 + 3x

Now, we can substitute this expression for y in the second equation:

4x - 3(2 + 3x) = -16

Distribute the -3:

4x - 6 - 9x = -16

Combine like terms:

-5x - 6 = -16

Add 6 to both sides:

-5x = -10

Divide both sides by -5:

x = 2

Now that we have the value of x, we can substitute it back into the first equation to solve for y:

y = 2 + 3(2)

y = 2 + 6

y = 8

Therefore, the solution to the system of equations is x = 2 and y = 8.
Answered by GPT 3.5
The solution to the system of equations is (2, 8).
Answered by GPT 3.5
To solve the system of equations, we can use the second equation and substitute the value of x into the first equation.

Substituting x = 5y - x into the first equation 2x + 6y = -18, we get:
2(5y - x) + 6y = -18.

Expanding and simplifying, we have:
10y - 2x + 6y = -18,
16y - 2x = -18.

Now, we can multiply the entire equation by -1/2 to make the coefficient of x positive:
(-1/2)(16y - 2x) = (-1/2)(-18),
-8y + x = 9.

Now, we have a system of equations:
-8y + x = 9,
2x + 6y = -18.

We can solve this system of equations using different techniques, such as substitution or elimination. Let's solve it using elimination:

Multiply the first equation by 2 to make the coefficients of x the same:
2(-8y + x) = 2(9),
-16y + 2x = 18.

Now our system of equations is:
-16y + 2x = 18,
2x + 6y = -18.

Adding the two equations, we get:
(-16y + 2x) + (2x + 6y) = 18 + (-18),
-10y = 0,
y = 0.

Substituting this value of y into the second equation, we can solve for x:
2x + 6(0) = -18,
2x = -18,
x = -9.

Therefore, the solution to the system of equations is (-9, 0).
Answered by GPT 3.5
To solve the system of linear equations, we can use the method of elimination:

Multiply the second equation by -1 to make the coefficients of x the same:
-1(3x - 5y) = -1(5)
-3x + 5y = -5

Now, our system of equations is:
-3x - 4y = -23
-3x + 5y = -5

Add the two equations:
(-3x - 4y) + (-3x + 5y) = -23 + (-5)
-6x + y = -28

Now, we have two equations:
-6x + y = -28
-3x - 4y = -23

Next, we can solve these equations using elimination. Multiply the first equation by -4 and the second equation by -1 to make the coefficients of y the same:

-4(-6x + y) = -4(-28)
4(3x + 4y) = 4(23)

Simplifying, we have:
24x - 4y = 112
12x + 16y = 92

Now, add the two equations:
(24x - 4y) + (12x + 16y) = 112 + 92
36x + 12y = 204

Divide the equation by 12 to simplify it:
3x + y = 17

Now, we have two equations:
3x + y = 17
-3x - 4y = -23

Adding the two equations eliminates x:
(3x + y) + (-3x - 4y) = 17 + (-23)
-3y = -6

Divide by -3:
y = 2

Substitute y = 2 into one of the equations to solve for x:
3x + 2 = 17
3x = 15
x = 5

Therefore, the solution to the system of equations is x = 5 and y = 2.
Answered by GPT 3.5
My apologies for the oversight. The solution to the system of equations is (5, 2).
Answered by GPT 3.5
The given system of equations is:

8x - 6y = 48
8x + 6y = 48

To determine the number of solutions, we can compare the equations and see if they represent parallel lines, the same line, or intersect at a single point.

By subtracting the first equation from the second equation, we get:

(8x + 6y) - (8x - 6y) = 48 - 48
12y = 0

Dividing both sides by 12, we have:

y = 0

Substituting this value of y into either of the equations, we find:

8x - 6(0) = 48
8x = 48
x = 6

Therefore, the two equations represent the same line, and there is an infinite number of solutions. The solution set can be expressed as (x, y) = (6, 0).
Answered by GPT 3.5
To solve the system of equations:

4x - 6y = -48
-2x + 4y = 30

We can multiply the second equation by 2 to make the coefficients of x the same:

(2)(-2x + 4y) = (2)(30)
-4x + 8y = 60

Now, our system of equations is:

4x - 6y = -48
-4x + 8y = 60

Adding the two equations eliminates x:

(4x - 6y) + (-4x + 8y) = -48 + 60
2y = 12

Dividing by 2, we find:

y = 6

Substituting this value of y into the first equation to solve for x:

4x - 6(6) = -48
4x - 36 = -48
4x = -12
x = -3

Therefore, the solution to the system of equations is (-3, 6).
Answered by GPT 3.5
To solve the system of equations:

3x - 4y = 40
5x - 5y = 55

We can solve this system of equations using the method of substitution:

From the first equation, we can solve for x in terms of y:
3x = 4y + 40
x = (4y + 40)/3

Now, we substitute this expression for x into the second equation:
5((4y + 40)/3) - 5y = 55

Multiplying both sides of the equation by 3 to eliminate the fraction, we get:
5(4y + 40) - 15y = 165

Expanding and simplifying:
20y + 200 - 15y = 165
5y + 200 = 165
5y = -35
y = -7

Now, substitute this value of y into the first equation to solve for x:
3x - 4(-7) = 40
3x + 28 = 40
3x = 12
x = 4

Therefore, the solution to the system of equations is (4, -7).