using substitution how to solve
x + 4y = 8
2x + 5y = 29
x = 8 - 4y
2x + 5y = 29
Substitute 8-4y for x in second equation and solve for y. Insert that value into the first equation and solve for x. Check by inserting both values into the second equation.
To solve the 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, x + 4y = 8, for x.
x = 8 - 4y
Step 2: Substitute the expression for that variable into the other equation.
Substitute x = 8 - 4y into the second equation, 2x + 5y = 29.
2(8 - 4y) + 5y = 29
Step 3: Simplify and solve for the remaining variable.
Expand and simplify the equation:
16 - 8y + 5y = 29
Combine like terms:
16 - 3y = 29
Subtract 16 from both sides:
-3y = 29 - 16
-3y = 13
Divide both sides by -3:
y = -13/3
Step 4: Substitute the value of y back into one of the original equations to find the value of x.
Using x + 4y = 8:
x + 4(-13/3) = 8
Multiply 4 by (-13/3):
x - 52/3 = 8
To simplify the equation, we need to obtain a common denominator:
Multiply both sides by 3 to eliminate the fraction:
3x - 52 = 24
Add 52 to both sides:
3x = 24 + 52
3x = 76
Divide both sides by 3:
x = 76/3
Therefore, the solution to the system of equations is x = 76/3 and y = -13/3.
To solve the given system of equations using the substitution method, follow these steps:
1. Solve one of the equations for one variable in terms of the other variable. Let's solve the first equation for x in terms of y:
x = 8 - 4y
2. Substitute the expression for x obtained in step 1 into the second equation:
2(8 - 4y) + 5y = 29
3. Simplify and solve the resulting equation for y:
16 - 8y + 5y = 29
-3y = 29 - 16
-3y = 13
y = 13 / -3
y = -4.33 (rounded to two decimal places)
4. Substitute the value of y back into either of the original equations. Let's use the first equation:
x + 4(-4.33) = 8
x - 17.32 = 8
x = 8 + 17.32
x = 25.32 (rounded to two decimal places)
Therefore, the solution to the system of equations is x = 25.32 and y = -4.33.