Solve the system of two equations using substitution. y=2+3x 4x−3y=−16 (1 point) Responses (−2, 4) left parenthesis negative 2 comma 4 right parenthesis (−2, −4) left parenthesis negative 2 comma negative 4 right parenthesis (2, 8) left parenthesis 2 comma 8 right parenthesis (2, 10)
To solve the system of equations using substitution, we start by solving one equation for one variable and then substitute this value into the second equation.
Given equations:
1) y = 2 + 3x
2) 4x - 3y = -16
Step 1: Solve equation (1) for y:
Rearrange equation (1) to isolate y:
y = 2 + 3x
Step 2: Substitute this value for y into equation (2):
4x - 3(2 + 3x) = -16
Distribute the -3:
4x - 6 - 9x = -16
Combine like terms:
-5x - 6 = -16
Step 3: Isolate x:
Add 6 to both sides:
-5x = -10
Divide both sides by -5:
x = 2
Step 4: Substitute this value for x into equation (1) to find y:
y = 2 + 3(2) = 2 + 6 = 8
Therefore, the solution to the system of equations is (2, 8).
Solve the system of equations. 2x+6y=−18 x=5y−1 (1 point) Responses (4, 1) left parenthesis 4 comma 1 right parenthesis (−7.25, −1.25) left parenthesis negative 7.25 comma negative 1.25 right parenthesis (−6, −1) left parenthesis negative 6 comma negative 1 right parenthesis (5.25, 1.25)
To solve the system of equations, we can substitute the value of x from equation (2) into equation (1).
Given equations:
1) 2x + 6y = -18
2) x = 5y - 1
Step 1: Substitute the value of x from equation (2) into equation (1):
2(5y - 1) + 6y = -18
Distribute the 2:
10y - 2 + 6y = -18
Step 2: Combine like terms:
16y - 2 = -18
Step 3: Isolate y:
Add 2 to both sides:
16y = -16
Divide both sides by 16:
y = -1
Step 4: Substitute this value for y back into equation (2) to find x:
x = 5(-1) - 1
x = -5 - 1
x = -6
Therefore, the solution to the system of equations is (-6, -1).
Solve the system of equations. 3x+y=2 7x−4y=30 (1 point) Responses (−2, 8) left parenthesis negative 2 comma 8 right parenthesis (12, 12) left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis (2, −4) left parenthesis 2 comma negative 4 right parenthesis (2, −2)
To solve the system of equations, we can use the method of substitution.
Given equations:
1) 3x + y = 2
2) 7x - 4y = 30
Step 1: Solve equation (1) for y:
y = 2 - 3x
Step 2: Substitute this value for y into equation (2):
7x - 4(2 - 3x) = 30
Distribute the -4:
7x - 8 + 12x = 30
Combine like terms:
19x - 8 = 30
Step 3: Isolate x:
Add 8 to both sides:
19x = 38
Divide both sides by 19:
x = 2
Step 4: Substitute this value for x into equation (1) to find y:
3(2) + y = 2
6 + y = 2
y = -4
Therefore, the solution to the system of equations is (2, -4).
Solve the system of equations. −4x+6y=38 x−5y=−20(1 point) Responses (−35, −3) left parenthesis negative 35 comma negative 3 right parenthesis (35, −3) left parenthesis 35 comma negative 3 right parenthesis (5, 3) left parenthesis 5 comma 3 right parenthesis (−5, 3)
To solve the system of equations, we can use the method of substitution.
Given equations:
1) -4x + 6y = 38
2) x - 5y = -20
Step 1: Solve equation (2) for x:
x = -20 + 5y
Step 2: Substitute this value for x into equation (1):
-4(-20 + 5y) + 6y = 38
Distribute the -4:
80 - 20y + 6y = 38
Simplify:
80 - 14y = 38
Step 3: Isolate y:
Subtract 80 from both sides:
-14y = -42
Divide both sides by -14:
y = 3
Step 4: Substitute this value for y 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).
How many solution(s) does the system of equations have? −5x+y=−18 10x−2y=36 (1 point) Responses one one two two infinite infinite none
To determine the number of solutions the system of equations has, we can analyze the slopes of the two equations.
Given equations:
1) -5x + y = -18
2) 10x - 2y = 36
Step 1: Rearrange equation (1) to slope-intercept form:
y = 5x - 18
Step 2: Rearrange equation (2) to slope-intercept form:
y = 5x - 18
Comparing the two equations, we can see that they have the same slope (5) and the same y-intercept (-18). This means the two lines are parallel and will never intersect.
Since the lines do not intersect, the system of equations has no solution.
Therefore, the system of equations has no solution.
To solve the system of two equations using substitution, we start by isolating one variable in one of the equations and then substitute it into the other equation.
Let's take the first equation: y = 2 + 3x
We can isolate y by subtracting 3x from both sides:
y - 3x = 2
Now, let's solve the second equation: 4x - 3y = -16
We will substitute y with the expression we found in the first equation:
4x - 3(2 + 3x) = -16
Distribute the -3 to both terms inside the parentheses:
4x - 6 - 9x = -16
Combine like terms:
-5x - 6 = -16
To isolate x, we will add 6 to both sides:
-5x = -10
Divide both sides by -5:
x = 2
Now that we have found the value of x, we can substitute it back into either of the original equations to find the value of y.
Let's use the first equation:
y = 2 + 3x
Substituting x = 2 into the equation:
y = 2 + 3(2)
y = 2 + 6
y = 8
Therefore, the solution to the system of equations is (2, 8).