Solve the system of two equations using substitution. y=2+3x 4x−3y=−16(1 point) Responses (2, 10) left parenthesis 2 comma 10 right parenthesis (2, 8) left parenthesis 2 comma 8 right parenthesis (−2, 4) left parenthesis negative 2 comma 4 right parenthesis (−2, −4)

Answer 1

First, we can substitute the value 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 x = 2, we can substitute this 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 (2, 8).

Answer 2

wrong

Answer 3

Let's try solving the system of equations again using substitution:

Given equations:
y = 2 + 3x
4x - 3y = -16

Substitute the expression for y in the second equation:
4x - 3(2 + 3x) = -16
4x - 6 - 9x = -16
-5x = -10
x = 2

Now, substitute the value of x back into the first equation to find y:
y = 2 + 3(2)
y = 2 + 6
y = 8

Therefore, the correct solution to the system of equations is (2, 8).

Answer 4

Solve the system of equations. 2x+6y=−18 x=5y−1(1 point) Responses (−6, −1) left parenthesis negative 6 comma negative 1 right parenthesis (4, 1) left parenthesis 4 comma 1 right parenthesis (5.25, 1.25) left parenthesis 5.25 comma 1.25 right parenthesis (−7.25, −1.25)

Answer 5

Given equations:
2x + 6y = -18
x = 5y - 1

Substitute 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, substituting y back into the second equation to solve for x:
x = 5(-1) - 1
x = -5 - 1
x = -6

Therefore, the solution to the system of equations is (-6, -1). So, the correct response is (-6, -1).

Answer 6

Solve the system of equations. 3x+y=2 7x−4y=30 (1 point) Responses (12, 12) left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis (2, −2) left parenthesis 2 comma negative 2 right parenthesis (2, −4) left parenthesis 2 comma negative 4 right parenthesis (−2, 8)

Answer 7

Given equations:
1. 3x + y = 2
2. 7x - 4y = 30

From the first equation, isolate y:
y = 2 - 3x

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 x = 2 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 (2, -4). So, the correct response is (2, -4).

Answer 8

Solve the system of equations. −4x+6y=38 x−5y=−20 (1 point) Responses (−5, 3) left parenthesis negative 5 comma 3 right parenthesis (5, 3) left parenthesis 5 comma 3 right parenthesis (−35, −3) left parenthesis negative 35 comma negative 3 right parenthesis (35, −3)

Answer 9

Given equations:
1. -4x + 6y = 38
2. x - 5y = -20

Let's solve the system of equations using substitution:

From equation 2:
x = 5y - 20

Substitute x from the equation above into equation 1:
-4(5y - 20) + 6y = 38
-20y + 80 + 6y = 38
-14y + 80 = 38
-14y = -42
y = 3

Now substitute y back into equation 2 to find x:
x = 5(3) - 20
x = 15 - 20
x = -5

Therefore, the solution to the system of equations is (-5, 3). So, the correct response is (-5, 3).