What is the solution of the system of equations?

13x−6y=2
3x−4y=−10



Enter your answer in the boxes.

13 x − 6 y = 2 Multiply both sides by 4

52 x - 24 y = 8

3 x − 4 y = − 10 Multiply both sides by - 6

- 18 x + 24 y = 60

Now solve system:

52 x - 24 y = 8

- 18 x + 24 y = 60

52 x - 24 y = 8
+
- 18 x + 24 y = 60
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34 x + 0 = 68

34 x = 68 Divide both sides by 34

x = 68 / 34 = 2

3 x − 4 y = − 10

3 * 2 - 4 y = - 10

6 - 4 y = - 10 Subtract 6 to both sides

6 - 4 y - 6 = - 10 - 6

- 4 y = - 16 Divide both sides by - 4

y = - 16 / - 4 = 4

Solution:

x = 2 , y = 4

To solve the system of equations:

Step 1: Choose a method to solve the system. One common method is substitution.

Step 2: Solve one equation for one variable in terms of the other variable, then substitute that expression into the other equation.

Let's solve the first equation, 13x - 6y = 2, for x:
13x = 6y + 2
Divide both sides of the equation by 13:
x = (6y + 2)/13

Step 3: Substitute the expression for x into the second equation, 3x - 4y = -10:
3((6y + 2)/13) - 4y = -10
Multiply through by 13 to eliminate the denominator:
18y + 6 - 52y = -130
Combine like terms:
-34y + 6 = -130
Subtract 6 from both sides:
-34y = -136
Divide both sides by -34:
y = 4

Step 4: Substitute the value of y back into the expression for x:
x = (6(4) + 2)/13
Simplify:
x = 26/13
x = 2

The solution to the system of equations is x = 2, y = 4.

To find the solution of the system of equations, we can use either the substitution method or the elimination method.

Let's use the elimination method:
First, we need to multiply the second equation by 2 to make the coefficients of x in both equations the same:

(2) * (3x - 4y) = (2) * (-10)
6x - 8y = -20

Now we have a system of equations:
13x - 6y = 2
6x - 8y = -20

Next, we can choose to eliminate either x or y from the equations. In this case, let's eliminate y. We can do this by multiplying the first equation by 4 and the second equation by 3:

(4) * (13x - 6y) = (4) * (2)
52x - 24y = 8

(3) * (6x - 8y) = (3) * (-20)
18x - 24y = -60

Now we have a new system of equations:
52x - 24y = 8
18x - 24y = -60

When we subtract the second equation from the first equation, the y terms will cancel out:

(52x - 24y) - (18x - 24y) = 8 - (-60)
52x - 24y - 18x + 24y = 8 + 60
34x = 68

Dividing both sides of the equation by 34:
34x/34 = 68/34
x = 2

Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:

13x - 6y = 2
13(2) - 6y = 2
26 - 6y = 2

Now, solve for y:

-6y = 2 - 26
-6y = -24
y = (-24)/(-6)
y = 4

Therefore, the solution to the system of equations is x = 2 and y = 4.