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
__________________
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.