To solve the system of equations using substitution, we can start by expressing one variable in terms of the other and then substituting this expression into the other equation.
In this case, let's solve the first equation, y = 2 + 3x, for y.
Substitute the expression for y into the second equation:
4x - 3y = -16
4x - 3(2 + 3x) = -16
Distribute the -3 through the parentheses:
4x - 6 - 9x = -16
Combine like terms:
-5x - 6 = -16
Add 6 to both sides of the equation:
-5x = -10
Divide both sides by -5:
x = 2
Now that we have the value of x, we can substitute it back into the first equation to solve for y:
y = 2 + 3x
y = 2 + 3(2)
y = 2 + 6
y = 8
Thus, the solution to the system of equations is (2, 8).
Solve the system of two equations using substitution. y=2+3x 4x−3y=−16 (1 point) Responses (−2, −4) left parenthesis negative 2 comma negative 4 right parenthesis (2, 8) left parenthesis 2 comma 8 right parenthesis (2, 10) left parenthesis 2 comma 10 right parenthesis (−2, 4) left parenthesis negative 2 comma 4 right
5 answers
Solve the system of equations. 2x+6y=−18 x=5y−1 (1 point) Responses (5.25, 1.25) left parenthesis 5.25 comma 1.25 right parenthesis (−7.25, −1.25) left parenthesis negative 7.25 comma negative 1.25 right parenthesis (4, 1) left parenthesis 4 comma 1 right parenthesis (−6, −1)
To solve the system of equations, we can substitute the expression for x in terms of y from the second equation into the first equation.
Given:
2x + 6y = -18
x = 5y - 1
Substitute the expression for x into the first equation:
2(5y - 1) + 6y = -18
Simplify:
10y - 2 + 6y = -18
16y - 2 = -18
Add 2 to both sides of the equation:
16y = -16
Divide both sides by 16:
y = -1
Now that we have the value of y, we can substitute it back into the second equation to solve for x:
x = 5y - 1
x = 5(-1) - 1
x = -5 - 1
x = -6
Thus, the solution to the system of equations is (-6, -1).
Given:
2x + 6y = -18
x = 5y - 1
Substitute the expression for x into the first equation:
2(5y - 1) + 6y = -18
Simplify:
10y - 2 + 6y = -18
16y - 2 = -18
Add 2 to both sides of the equation:
16y = -16
Divide both sides by 16:
y = -1
Now that we have the value of y, we can substitute it back into the second equation to solve for x:
x = 5y - 1
x = 5(-1) - 1
x = -5 - 1
x = -6
Thus, the solution to the system of equations is (-6, -1).
solving equations using substitution quick check 3 of 53 of 5 items question solve the system of equations. 3x+y=2 7x−4y=30 (1 point) responses (2, −4) left parenthesis 2 comma negative 4 right parenthesis (−2, 8) left parenthesis negative 2 comma 8 right parenthesis (2, −2) left parenthesis 2 comma negative 2 right parenthesis (12, 12)
To solve the system of equations using substitution, we can start by expressing one variable in terms of the other and then substituting this expression into the other equation.
Let's solve the first equation, 3x + y = 2, for y:
y = 2 - 3x
Now, substitute this expression for y into the second equation:
7x - 4(2 - 3x) = 30
Simplify and solve for x:
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 2
Now that we have the value of x, we can substitute it back into the first equation to solve for y:
3x + y = 2
3(2) + y = 2
6 + y = 2
y = -4
Thus, the solution to the system of equations is (2, -4).
Let's solve the first equation, 3x + y = 2, for y:
y = 2 - 3x
Now, substitute this expression for y into the second equation:
7x - 4(2 - 3x) = 30
Simplify and solve for x:
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 2
Now that we have the value of x, we can substitute it back into the first equation to solve for y:
3x + y = 2
3(2) + y = 2
6 + y = 2
y = -4
Thus, the solution to the system of equations is (2, -4).