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

Answer 1

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

Starting with the second equation, x=5y-1, we can substitute this expression for x in the first equation:

2x + 6y = -18

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

10y - 2 + 6y = -18

Combine like terms:

16y - 2 = -18

Add 2 to both sides:

16y = -16

Divide both sides by 16:

y = -1

Now, substitute this value of y back into the second equation to solve for x:

x = 5y - 1

x = 5(-1) - 1

x = -5 - 1

x = -6

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

Answer 2

Solve the system of equations. 3x+y=2 7x−4y=30 (1 point)

Answer 3

To solve the system of equations, we can use the method of substitution or elimination. Here, we will use elimination.

First, multiply the first equation by 4 and the second equation by 1 so that the coefficients of the y terms will cancel each other out.

4(3x + y) = 4(2)
1(7x - 4y) = 1(30)

Simplifying, we have:

12x + 4y = 8
7x - 4y = 30

Now, add the two equations together to eliminate the y term:

(12x + 4y) + (7x - 4y) = 8 + 30

12x + 4y + 7x - 4y = 38

Combining like terms, we get:

19x = 38

Divide both sides by 19:

x = 38/19

Simplifying, we have:

x = 2

Now substitute this value of x back into either of the original equations:

3x + y = 2
3(2) + y = 2
6 + y = 2
y = 2 - 6
y = -4

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