Use substitution method to solve.
(1/2x)+(3/4y)=(-1/4) and (3/4x)-(1/4y)=1
Can you please help?
first, I'd get rid of those pesky fractions:
2x + 3y = -1
3x - y = 4
Now you can see that y = 3x-4, so substitute that back in the 1st equation:
2x + 3(3x-4) = -1
2x+9x-12 = -1
11x = 11
x = 1
so, y=3x-4 = -1
be sure to check that the answer fits the original equations.
Thank you.
Sure! To solve this system of equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation for x:
(1/2x) + (3/4y) = (-1/4)
Multiplying both sides of the equation by 2 to clear the denominator, we get:
x + (3/2)y = (-1/2)
Rearranging the equation, we have:
x = (-1/2) - (3/2)y
Step 2: Substitute the expression for x obtained in step 1 into the other equation.
Substituting x = (-1/2) - (3/2)y into the second equation, we get:
(3/4)((-1/2) - (3/2)y) - (1/4)y = 1
Multiplying through by 4 to eliminate the denominators, we have:
3(-1/2 - (3/2)y) - y = 4
Simplifying, we get:
-3/2 - (9/2)y - y = 4
Combining like terms, we have:
- (11/2)y - 3/2 = 4
Adding 3/2 to both sides, we get:
-(11/2)y = 11/2
Dividing by -11/2, we have:
y = -1
Step 3: Substitute the value of y obtained in step 2 back into either of the original equations to solve for x.
Substituting y = -1 into the first equation, we get:
(1/2x) + (3/4(-1)) = (-1/4)
Simplifying, we have:
(1/2)x - (3/4) = (-1/4)
Adding (3/4) to both sides, we get:
(1/2)x = 0
Dividing by (1/2), we have:
x = 0
So, the solution to the system of equations is x = 0 and y = -1.