Solve the system of equations.
7x+3y=−25
−7x+9y=−47 (1 point)
Make shore is correct
To solve the system of equations:
1) Start by adding the two equations together to eliminate the term "x":
(7x + 3y) + (-7x + 9y) = -25 + (-47)
3y + 9y = -25 - 47
12y = -72
2) Divide both sides of the equation by 12 to isolate "y":
12y/12 = -72/12
y = -6
3) Substitute the value of "y" back into one of the original equations to solve for "x". We'll use the first equation:
7x + 3(-6) = -25
7x - 18 = -25
4) Add 18 to both sides of the equation:
7x - 18 + 18 = -25 + 18
7x = -7
5) Divide both sides of the equation by 7 to solve for "x":
7x/7 = -7/7
x = -1
Therefore, 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 terms.
7(7x + 3y) = 7(-25)
49x + 21y = -175 (Equation A)
Step 2: Multiply the second equation by -7 to eliminate the x terms.
-7(-7x + 9y) = -7(-47)
49x - 63y = 329 (Equation B)
Step 3: Add Equation A and Equation B together.
(49x + 21y) + (49x - 63y) = - 175 + 329
98x - 42y = 154
Step 4: Simplify the equation.
Divide both sides of the equation by 14 to simplify the coefficients.
(98/14)x - (42/14)y = 154/14
7x - 3y = 11 (Equation C)
Step 5: Now we have two equations:
7x + 3y = -25 (Equation 1)
7x - 3y = 11 (Equation 2)
Step 6: Add the two equations together to eliminate the x terms.
(7x + 3y) + (7x - 3y) = -25 + 11
14x = -14
Step 7: Divide both sides of the equation by 14 to solve for x.
x = -14/14
x = -1
Step 8: Substitute the value of x into either Equation 1 or Equation 2 and solve for y. Let's use Equation 1.
7(-1) + 3y = -25
-7 + 3y = -25
3y = -25 + 7
3y = -18
Step 9: Divide both sides of the equation by 3 to solve for y.
y = -18/3
y = -6
Therefore, the solution to the system of equations is x = -1 and y = -6.
To solve the system of equations, we can either use the substitution method or the elimination method. Let's use the elimination method in this case.
We have the given system of equations:
Equation 1: 7x + 3y = -25
Equation 2: -7x + 9y = -47
To eliminate one variable, we can multiply both sides of Equation 1 by 7 and Equation 2 by -7. This will result in equations with opposite coefficients for the x-term:
Equation 1 (multiplied by 7): 49x + 21y = -175
Equation 2 (multiplied by -7): 49x - 63y = 329
Now, we can add the two equations together to eliminate the x-term:
(49x + 21y) + (49x - 63y) = (-175) + (329)
98x - 42y = 154
Simplifying further, we divide both sides of the equation by 2 to get:
49x - 21y = 77
Now, we have a new equation:
Equation 3: 49x - 21y = 77
Next, we can solve this new equation simultaneously with Equation 1:
Equation 1: 7x + 3y = -25
Multiply Equation 1 by 7:
(7x + 3y) * 7 = (-25) * 7
49x + 21y = -175
We can see that Equation 1 and Equation 3 are identical. This means that the two equations are dependent and represent the same line. Therefore, there are infinitely many solutions.
The solution to the system of equations is any pair of values (x, y) that satisfies the equations.