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, 8)
left parenthesis negative 2 comma 8 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 or elimination.
Using the substitution method, we can solve one equation for one variable and then substitute that expression into the other equation.
From the first equation, we can solve for y in terms of x:
3x + y = 2
y = 2 - 3x
Now we substitute this value of y into the second equation:
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 2
Now we substitute this value of x back into the first equation to solve for 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.
1. Start with the first equation: 3x + y = 2.
2. Solve for y: y = 2 - 3x.
3. Substitute the value of y in the second equation: 7x - 4(2 - 3x) = 30.
4. Simplify the equation: 7x - 8 + 12x = 30.
5. Combine like terms: 19x - 8 = 30.
6. Add 8 to both sides: 19x = 38.
7. Divide both sides by 19: x = 2.
8. Substitute the value of x into the first equation: 3(2) + y = 2.
9. Simplify: 6 + y = 2.
10. Subtract 6 from both sides: 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 elimination. Here's how to do it step by step:
Step 1: Multiply the first equation by 4.
3x + y = 2 (equation 1)
4(3x + y) = 4(2)
12x + 4y = 8
Step 2: Multiply the second equation by 3.
7x - 4y = 30 (equation 2)
3(7x - 4y) = 3(30)
21x - 12y = 90
Step 3: Add equation 1 and equation 2 together to eliminate y.
(12x + 4y) + (21x - 12y) = 8 + 90
33x - 8y = 98
Step 4: Solve the resulting equation.
33x - 8y = 98
There are several ways to solve this equation, but one common method is substitution. To do substitution, we'll isolate one variable and substitute it into the other equation.
Let's isolate y in equation 1:
3x + y = 2
y = 2 - 3x
Now substitute this value of y into equation 2:
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 2
Step 5: Substituting the value of x back 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).