Solve the system of equations 7x+3y=-25 and -7x+9y=-47
To solve the system of equations, we'll use the method of elimination.
First, let's add the two equations together to eliminate the x term:
(7x + 3y) + (-7x + 9y) = -25 + (-47)
7x + 3y - 7x + 9y = -72
12y = -72
y = -72/12
y = -6
Now substitute the value of y back into one of the original equations to solve for x:
7x + 3(-6) = -25
7x - 18 = -25
7x = -25 + 18
7x = -7
x = -7/7
x = -1
So the solution to the system of equations is x = -1 and y = -6.
To solve the system of equations:
Step 1: Multiply the first equation by 7 to eliminate the x term.
7x + 3y = -25
7(7x + 3y) = 7(-25)
49x + 21y = -175
Step 2: Multiply the second equation by -1 to eliminate the x term.
-7x + 9y = -47
-1(-7x + 9y) = -1(-47)
7x - 9y = 47
Step 3: Add the two equations together to eliminate the x term.
(49x + 21y) + (7x - 9y) = -175 + 47
49x + 21y + 7x - 9y = -128
56x + 12y = -128
Step 4: Divide both sides of the equation by 4 to simplify.
(56x + 12y) / 4 = -128 / 4
14x + 3y = -32
So, the system of equations simplifies to:
14x + 3y = -32 (1)
7x - 9y = 47 (2)
The solution to this system is (x, y) = (-3, -2).
To solve the system of equations:
1. Start by eliminating one variable. Add the two equations together to eliminate "x":
(7x + 3y) + (-7x + 9y) = -25 + (-47)
Simplifying gives:
3y + 9y = -25 - 47
12y = -72
2. Solve for "y" by dividing both sides of the equation by 12:
y = -72 / 12
y = -6
3. Substitute the value of "y" back into one of the original equations to find the value of "x". Let's use the first equation:
7x + 3(-6) = -25
Simplifying gives:
7x - 18 = -25
4. Move the constant to the other side by adding 18 to both sides:
7x = -25 + 18
7x = -7
5. Solve for "x" by dividing both sides by 7:
x = -7 / 7
x = -1
Therefore, the solution to the system of equations is x = -1 and y = -6.