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)
left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis
The correct 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 elimination:
Step 1: Multiply the first equation by 4 to make the coefficient of "y" the same in both equations:
4 * (3x + y) = 4 * 2
12x + 4y = 8
Step 2: Rewrite the second equation:
7x - 4y = 30
Step 3: Add the two equations:
(12x + 4y) + (7x - 4y) = 8 + 30
12x + 7x = 38
19x = 38
Step 4: Solve for "x":
19x/19 = 38/19
x = 2
Step 5: Substitute the value of "x" back into either equation to solve for "y". Let's substitute it into the first equation:
3x + y = 2
3(2) + y = 2
6 + y = 2
y = 2 - 6
y = -4
Therefore, the solution to the system of equations is (2, -4).
To solve the system of equations:
1. Start by the method of elimination. Multiply the first equation by 4 to make the coefficients of "y" in both equations the same:
12x + 4y = 8
2. Subtract the modified first equation from the second equation to eliminate the variable "y":
(7x - 4y) - (12x + 4y) = 30 - 8
-5x = 22
x = -4.4
3. Substitute the value of "x" into either of the original equations. Let's use the first equation:
3x + y = 2
3(-4.4) + y = 2
-13.2 + y = 2
y = 2 + 13.2
y = 15.2
4. The solution to the system of equations is (x, y) = (-4.4, 15.2).
Therefore, the correct response is: (−4.4, 15.2) or (-4.4, 15.2).