Solve the system of equations. 3x+y=2. 7x-4y=30
To solve the system of equations, we can use the method of substitution.
From the first equation, we can solve for y in terms of x:
Given 3x + y = 2, we can subtract 3x from both sides to isolate y:
y = 2 - 3x
Now, we can substitute this value of y into the second equation:
7x - 4(2 - 3x) = 30
Simplifying this equation:
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 38/19
x = 2
To find y, we substitute this value of x into the first equation:
3(2) + y = 2
6 + y = 2
y = 2 - 6
y = -4
Therefore, the solution to the system of equations is x = 2 and y = -4.
To solve the system of equations:
3x + y = 2 ...(Equation 1)
7x - 4y = 30 ...(Equation 2)
We can solve this system of equations using the method of substitution. Let's solve Equation 1 for y:
3x + y = 2
y = 2 - 3x
Now, we substitute this value of y in Equation 2:
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
Next, we isolate x by moving the constant term to the right side:
19x = 30 + 8
19x = 38
Then, divide both sides by 19 to solve for x:
x = 38/19
x = 2
Now that we have the value of x, we can substitute it back into Equation 1 to solve for y:
3(2) + y = 2
6 + y = 2
Subtract 6 from both sides to isolate y:
y = 2 - 6
y = -4
Therefore, the solution to the system of equations is x = 2 and y = -4.
To solve the system of equations, we can use either the substitution method or the elimination method. Let's use the elimination method in this case. The goal is to eliminate one variable by manipulating the equations so that when we add them or subtract them, one variable will cancel out.
Given the system of equations:
Equation 1: 3x + y = 2
Equation 2: 7x - 4y = 30
To eliminate the y variable, you can multiply Equation 1 by 4 and Equation 2 by 1, so that the coefficients of y will be opposites of each other.
4 * Equation 1: 12x + 4y = 8
1 * Equation 2: 7x - 4y = 30
Now, add the new equations together to eliminate y:
(12x + 4y) + (7x - 4y) = 8 + 30
Simplifying the equation, we get:
12x + 4y + 7x - 4y = 38
Combining like terms, we have:
19x = 38
Now, isolate the x variable by dividing both sides of the equation by 19:
19x / 19 = 38 / 19
x = 2
Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use Equation 1:
3x + y = 2
3 * 2 + y = 2
6 + y = 2
Subtracting 6 from both sides, we get:
y = -4
So the solution to the system of equations is x = 2 and y = -4.