First, substitute the value of x from the first equation into the second equation:
2(6y - 3) + 7y = 13
12y - 6 + 7y = 13
19y - 6 = 13
19y = 19
y = 1
Now, substitute the value of y back into the first equation to solve for x:
x = 6(1) - 3
x = 6 - 3
x = 3
Therefore, the solution to the system of equations is x = 3 and y = 1.
Solve the system of equations.
x = 6y - 3
2x + 7y = 13
(_,_)
show your work
5 answers
solve the system of equations.
8x - 3y = -22
y = 10 + 4x
(_,_)
show your work.
8x - 3y = -22
y = 10 + 4x
(_,_)
show your work.
To solve this system of equations, we can substitute the second equation into the first equation and then solve for x.
8x - 3(10 + 4x) = -22
8x - 30 - 12x = -22
-4x - 30 = -22
-4x = 8
x = -2
Now that we have found the value of x, we can substitute it back into the second equation to solve for y.
y = 10 + 4(-2)
y = 10 - 8
y = 2
Therefore, the solution to the system of equations is x = -2 and y = 2.
8x - 3(10 + 4x) = -22
8x - 30 - 12x = -22
-4x - 30 = -22
-4x = 8
x = -2
Now that we have found the value of x, we can substitute it back into the second equation to solve for y.
y = 10 + 4(-2)
y = 10 - 8
y = 2
Therefore, the solution to the system of equations is x = -2 and y = 2.
1. solve the system of equations.
5x + 2y = 14
x - 6y = 22
(_,_)
show your work.
2. solve the system of equations.
-9x + y = 12
2x + 4y = -28
(_,_)
show your work
5x + 2y = 14
x - 6y = 22
(_,_)
show your work.
2. solve the system of equations.
-9x + y = 12
2x + 4y = -28
(_,_)
show your work
1. To solve the first system of equations:
5x + 2y = 14
x - 6y = 22
We can use the method of substitution or elimination to find the values of x and y. Let's use the elimination method here:
1. Multiply the second equation by 2 to make the coefficients of y equal but opposite in signs:
2(x - 6y) = 2(22)
2x - 12y = 44
2. Add this new equation to the first equation:
5x + 2y + 2x - 12y = 14 + 44
7x - 10y = 58
3. Solve for x and y:
7x - 10y = 58
7x = 10y + 58
x = (10y + 58) / 7
5x + 2y = 14
5((10y + 58) / 7) + 2y = 14
50y/7 + 290/7 + 2y = 14
50y + 290 + 14y = 98
64y = -192
y = -3
Now that we have found the value of y, substitute it back into one of the equations to find x:
5x + 2(-3) = 14
5x - 6 = 14
5x = 20
x = 4
Therefore, the solution to the first system of equations is x = 4 and y = -3.
2. To solve the second system of equations:
-9x + y = 12
2x + 4y = -28
Let's again use the elimination method:
1. Multiply the first equation by 4 and the second equation by 1 to make the coefficients of y equal but opposite in signs:
-36x + 4y = 48
2x + 4y = -28
2. Add the two equations together:
-36x + 4y + 2x + 4y = 48 - 28
-34x = 20
x = -20/34 = -10/17
Now that we have found the value of x, substitute it back into one of the equations to find y:
-9(-10/17) + y = 12
90/17 + y = 12
y = 12 - 90/17
y = 204/17 - 90/17
y = 114/17
Therefore, the solution to the second system of equations is x = -10/17 and y = 114/17.
5x + 2y = 14
x - 6y = 22
We can use the method of substitution or elimination to find the values of x and y. Let's use the elimination method here:
1. Multiply the second equation by 2 to make the coefficients of y equal but opposite in signs:
2(x - 6y) = 2(22)
2x - 12y = 44
2. Add this new equation to the first equation:
5x + 2y + 2x - 12y = 14 + 44
7x - 10y = 58
3. Solve for x and y:
7x - 10y = 58
7x = 10y + 58
x = (10y + 58) / 7
5x + 2y = 14
5((10y + 58) / 7) + 2y = 14
50y/7 + 290/7 + 2y = 14
50y + 290 + 14y = 98
64y = -192
y = -3
Now that we have found the value of y, substitute it back into one of the equations to find x:
5x + 2(-3) = 14
5x - 6 = 14
5x = 20
x = 4
Therefore, the solution to the first system of equations is x = 4 and y = -3.
2. To solve the second system of equations:
-9x + y = 12
2x + 4y = -28
Let's again use the elimination method:
1. Multiply the first equation by 4 and the second equation by 1 to make the coefficients of y equal but opposite in signs:
-36x + 4y = 48
2x + 4y = -28
2. Add the two equations together:
-36x + 4y + 2x + 4y = 48 - 28
-34x = 20
x = -20/34 = -10/17
Now that we have found the value of x, substitute it back into one of the equations to find y:
-9(-10/17) + y = 12
90/17 + y = 12
y = 12 - 90/17
y = 204/17 - 90/17
y = 114/17
Therefore, the solution to the second system of equations is x = -10/17 and y = 114/17.