Solve the system of two linear equations.

Question

−3x−4y=−23
3x−5y=5 (1 point)??

Answer 1

First rewrite the equations in a more readable form.
Equation 1: -3x - 4y = -23
Equation 2: 3x - 5y = 5

Next, add both equations together to eliminate x:
(-3x - 4y) + (3x - 5y) = -23 + 5
-4y - 9y = -18
-9y = -18
y = 2

Now plug the solution for y back into Equation 1 to solve for x:
-3x - 4(2) = -23
-3x - 8 = -23
-3x = -15
x = 5

Thus, the solution to the system of linear equations is:
x = 5
y = 2

Answer 2

How many solutions does the system of equations have?
8x−6y=48
8x+6y=48 (1 point)

Answer 3

When we compare the two equations we can see that they are the same but one is multiplied by -1 and the other is not. Therefore, these are the same line and the system of equations has infinitely many solutions.

Answer 4

Solve the system of two equations using elimination with multiplication.
4x−6y=−48
−2x+4y=30 (1 point)
Responses

Answer 5

To solve this system of equations using elimination with multiplication, we need to decide which variable to eliminate first. Let's focus on eliminating the variable x.

First, you can see that the coefficients of x in the given equations are 4 and -2. To make them equal in magnitude but opposite in sign, we need to multiply the second equation by 2.

So, let's rewrite the system of equations with the second equation multiplied by 2:

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

Now, add the two equations together to eliminate x:

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

Now, we will substitute the value of y back into one of the equations to solve for x. Let's choose the first equation:

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

Therefore, the solution to the system of equations is:
x = -3
y = 6

Answer 6

Solve the system of equations.
3x−4y=40
5x−5y=55 (1 point)

Answer 7

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of elimination to solve this system.

Given equations:
1. 3x - 4y = 40
2. 5x - 5y = 55

First, let's multiply the first equation by 5 and the second equation by 3 to make the coefficients of x the same with opposite signs:

1. 15x - 20y = 200
2. 15x - 15y = 165

Now, we subtract equation 2 from equation 1:

(15x - 20y) - (15x - 15y) = 200 - 165
-5y = 35
y = -7

Now, substitute y = -7 into equation 1:

3x - 4(-7) = 40
3x + 28 = 40
3x = 12
x = 4

The solution to the system of equations is:
x = 4, y = -7

Answer 8

How many solutions does the system have?
12x−15y=18
4x−5y=6(1 point)
Responses

two solutions
two solutions

no solution
no solution

one solution
one solution

infinitely many solutions
infinitely many solutions

Answer 9

To determine how many solutions the system of equations has, let's analyze the given equations:

1) 12x - 15y = 18
2) 4x - 5y = 6

One way to determine the number of solutions is to check if the two equations are inconsistent (meaning they have no solution) or dependent (meaning they have infinite solutions) by comparing their slopes.

We can first simplify the equations by dividing each equation by a common factor to make it easier to analyze:

Equation 1:
4x - 5y = 6 (Divide by 2)
2x - 2.5y = 3

Equation 2:
4x - 5y = 6

Now compare the slopes of the simplified equations. Since the slopes are not equal and the y-intercepts are also different, we can conclude that the lines represented by the two equations are not parallel and do not coincide. Thus, the system of equations has one unique solution.

Therefore, the system of equations has only one solution.