Solve the system of equations.
7x+3y=−25
−7x+9y=−47 (1 point)
To solve this system of equations, we can use the method of elimination.
Multiply the first equation by 9 and the second equation by 3 to make the coefficients of x in both equations equal:
9(7x + 3y) = 9(-25) becomes 63x + 27y = -225
3(-7x + 9y) = 3(-47) becomes -21x + 27y = -141
Now we can add these two equations together to eliminate the x variable:
(63x + 27y) + (-21x + 27y) = (-225) + (-141)
42x = -366
Divide both sides of the equation by 42 to solve for x:
x = -366/42
x = -183/21
Substitute this value of x back into either of the original equations to solve for y. We'll use the first equation:
7x + 3y = -25
7(-183/21) + 3y = -25
-1281/21 + 3y = -25
3y = -25 + 1281/21
3y = (-525 + 1281)/21
3y = 756/21
3y = 36
y = 12
Therefore, the solution to the system of equations is x = -183/21 and y = 12.
To solve the system of equations, we will use the method of elimination.
Step 1: Multiply the first equation by 7 and the second equation by -7 to eliminate the x term.
7(7x+3y) = 7(-25)
-7(-7x+9y) = -7(-47)
Which simplifies to:
49x + 21y = -175
49x - 63y = 329
Step 2: Subtract the second equation from the first equation to eliminate the x term.
(49x + 21y) - (49x - 63y) = -175 - 329
Which simplifies to:
84y = -504
Step 3: Divide both sides of the equation by 84 to solve for y.
84y/84 = -504/84
y = -6
Step 4: Substitute the value of y into one of the original equations to solve for x.
7x + 3(-6) = -25
7x - 18 = -25
Step 5: Add 18 to both sides of the equation.
7x - 18 + 18 = -25 + 18
7x = -7
Step 6: Divide both sides of the equation by 7 to solve for x.
7x/7 = -7/7
x = -1
So the solution to the system of equations is x = -1 and y = -6.
To solve the system of equations, we will use the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the first equation for x:
7x + 3y = -25.
Subtract 3y from both sides:
7x = -25 - 3y.
Divide both sides by 7:
x = (-25 - 3y) / 7.
Step 2: Substitute the expression for x into the other equation.
Now, substitute the expression for x into the second equation:
-7((-25 - 3y) / 7) + 9y = -47.
Simplify the equation:
-25 - 3y + 9y = -47.
Combine like terms:
6y - 25 = -47.
Step 3: Solve for y.
Add 25 to both sides of the equation:
6y = -47 + 25.
Simplify:
6y = -22.
Divide both sides by 6:
y = -22 / 6.
Simplify:
y = -11 / 3.
Step 4: Substitute the value of y back into the expression for x.
Now that we have found the value of y, substitute it back into the expression for x:
x = (-25 - 3(-11/3)) / 7.
Simplify:
x = (-25 + 33/3) / 7.
x = (-25 + 11) / 7.
x = -14/7.
Simplify:
x = -2.
So, the solution to the system of equations is x = -2 and y = -11/3.