Slove the system of equations
7x+3y=-25
-7x+9y=-47
To solve this system of equations, we can use the method of elimination.
Start by adding the two equations together to eliminate the term "-7x":
(7x + 3y) + (-7x + 9y) = -25 + (-47)
7x - 7x + 3y + 9y = -25 - 47
12y = -72
Divide both sides of the equation by 12:
12y/12 = -72/12
y = -6
Now substitute the value of y back into one of the original equations, let's use the first equation:
7x + 3(-6) = -25
7x - 18 = -25
Add 18 to both sides of the equation:
7x - 18 + 18 = -25 + 18
7x = -7
Divide both sides of the equation by 7:
7x/7 = -7/7
x = -1
So the solution to the system of equations is x = -1, y = -6.
To solve the system of equations:
Step 1: Eliminate one variable:
Multiply the first equation by 7 and the second equation by -7 to eliminate x.
- 7x + 9y = -47 --> -49x + 63y = -329
Step 2: Add the equations together:
Add the new equations together to eliminate x.
(7x + 3y) + (-49x + 63y) = (-25) + (-329)
-42x + 66y = -354
Step 3: Solve for y:
Now you have a new equation with only y. Solve for y.
-42x + 66y = -354
66y = -354 + 42x
y = (-354 + 42x)/66
Step 4: Substitute y into one of the original equations:
Choose either of the original equations to substitute the value of y into.
Let's use the first equation since it is simpler.
7x + 3((-354 + 42x)/66) = -25
Step 5: Solve for x:
Now you have an equation with only x. Solve for x.
Multiply through by 66 to eliminate the fraction:
462x + 3(-354 + 42x) = -1650
462x - 1062 + 126x = -1650
588x - 1062 = -1650
588x = -1650 + 1062
588x = -588
x = -588/588
x = -1
Step 6: Solve for y:
Finally, substitute the value of x back into one of the original equations to solve for y. Let's use the first equation:
7(-1) + 3y = -25
-7 + 3y = -25
3y = -25 + 7
3y = -18
y = -18/3
y = -6
Therefore, the solution to the system of equations is x = -1 and y = -6.