Solve the system of equations.
3x+y=2
7x−4y=30(1 point)
Responses
(2, −2)
left parenthesis 2 comma negative 2 right parenthesis
(2, −4)
left parenthesis 2 comma negative 4 right parenthesis
(12, 12)
left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis
(−2, 8)
To solve the system of equations, let's use the method of substitution.
First, let's solve the first equation for y:
3x + y = 2
y = 2 - 3x
Now substitute the value of y in the second equation:
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 2
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 (2, -4).
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
Step 1: Solve one equation for one variable.
From the first equation, we can solve for y in terms of x:
3x + y = 2
y = 2 - 3x
Step 2: Substitute the expression we found for y into the second equation.
Substitute y = 2 - 3x into the second equation:
7x - 4(2 - 3x) = 30
Step 3: Simplify the second equation.
Distribute the -4:
7x - 8 + 12x = 30
Combine like terms:
19x - 8 = 30
Add 8 to both sides:
19x = 38
Divide both sides by 19:
x = 2
Step 4: Substitute the value of x into either equation to solve for y.
Using the first equation:
3(2) + y = 2
6 + y = 2
Subtract 6 from both sides:
y = -4
Therefore, the solution to the system of equations is (x, y) = (2, -4).
To solve the system of equations:
1. First, let's isolate one variable in one of the equations. We can do this by multiplying the first equation by 4 to cancel out the y term: 4(3x + y) = 4(2) => 12x + 4y = 8.
2. Now we have two equations:
- 12x + 4y = 8
- 7x - 4y = 30
3. Adding both equations together eliminates the y variable: (12x + 4y) + (7x - 4y) = 8 + 30 => 19x = 38.
4. Divide both sides of the equation by 19 to solve for x: 19x/19 = 38/19 => x = 2.
5. Substitute the value of x = 2 back into one of the original equations. Let's use the first equation: 3(2) + y = 2 => 6 + y = 2.
6. Solve for y by subtracting 6 from both sides of the equation: y = 2 - 6 => y = -4.
7. Therefore, the solution to the system of equations is (2, -4).