Solve the system of equations.

Question

x=6y−3

2x+7y=13

Answer 1

To solve this system of equations, we can replace the x value in the second equation with the expression from the first equation:

2(6y-3) + 7y = 13
12y - 6 + 7y = 13
19y - 6 = 13
19y = 19
y = 1

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

x = 6(1) - 3
x = 3

Therefore, the solution to the system of equations is x = 3 and y = 1.

Answer 2

Solve the system of two equations using substitution.
y=2+3x
4x−3y=−16

Answer 3

We will use substitution to solve this system of equations.

First, we will substitute the expression of y from the first equation into the second equation:

4x - 3(2 + 3x) = -16
4x - 6 - 9x = -16
-5x - 6 = -16
-5x = -10
x = 2

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

y = 2 + 3(2)
y = 2 + 6
y = 8

Therefore, the solution to the system of equations is x = 2 and y = 8.

Answer 4

Solve the system of equations.
2x+6y=−18
x=5y−1

Answer 5

We will solve this system of equations by substituting the expression x from the second equation into the first equation:

2(5y - 1) + 6y = -18
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -1

Now that we have found the value of y, we can substitute it back into the second equation to find the value of x:

x = 5(-1) - 1
x = -5 - 1
x = -6

Therefore, the solution to the system of equations is x = -6 and y = -1.

Answer 6

Solve the system of equations.
3x+y=2
7x−4y=30

Answer 7

To solve this system of equations, we can use the substitution method:

From the first equation, rearrange it to solve for y:
y = 2 - 3x

Now substitute this expression for y into the second equation:
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 2

Now substitute the value of x back into the first equation to find y:
3(2) + y = 2
6 + y = 2
y = -4

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

Answer 8

Solve the system of equations.
−4x+6y=38
x−5y=−20

Answer 9

To solve this system of equations, we can use the elimination method.

First, let's multiply the second equation by 4 to make the coefficients of x in both equations the same:

4x - 20y = -80

Now we have the system of equations:

-4x + 6y = 38
4x - 20y = -80

Adding these two equations together, we get:

-14y = -42
y = 3

Now substitute y = 3 back into the second equation:

x - 5(3) = -20
x - 15 = -20
x = -5

Therefore, the solution to the system of equations is x = -5 and y = 3.

Answer 10

How many solution(s) does the system of equations have?
−5x+y=−18
10x−2y=36

Answer 11

To determine how many solutions the system of equations has, we can use the elimination method.

-5x + y = -18
10x - 2y = 36

First, let's rewrite the second equation by dividing all terms by 2 to simplify it:

5x - y = 18

Now, we can see that if we multiply the first equation by 2, we get the same equation as the second equation. This means the two equations represent the same line and are dependent.

Therefore, the system of equations has infinitely many solutions as the two equations represent the same line.