Solve the equation by substitution method (y-1/4x=3,3y+x=23)
yes
y - 1 / 4 x = 3
3 y + x = 23
First equation:
y - 1 / 4 x = 3
Add 1 / 4 x to both sides
y = 3 + 1 / 4 x
Substitute y with 3 + 1 / 4 x in the second equation
3 y + x = 23
3 ( 3 + 1 / 4 x ) + x = 23
9 + 3 / 4 x + x = 23
9 + 3 / 4 x + 4 / 4 x = 23
9 + 7 / 4 x = 23
Subtract 9 to both sides
7 / 4 x = 14
Multiply both sides by 4
7 x = 56
Divide both sides by 7
x = 8
Substitute x with 8 in the first equation
y - 1 / 4 x = 3
y - 1 / 4 ∙ 8 = 3
y - 2 = 3
Add 2 to both sides
y = 5
The solution is ( 8 , 5 )
To solve the given system of equations using the substitution method, we will solve one equation for one variable and substitute it into the other equation. Let's begin:
Step 1: Solve the first equation for y.
y - (1/4)x = 3
First, let's isolate y by subtracting (1/4)x from both sides:
y = 3 + (1/4)x
Step 2: Substitute the value of y into the second equation.
3y + x = 23
Replace y with its value (3 + (1/4)x):
3(3 + (1/4)x) + x = 23
Step 3: Simplify and solve for x.
9 + (3/4)x + x = 23
Combine like terms:
(7/4)x + x = 23 - 9
(7/4)x + (4/4)x = 14
(11/4)x = 14
Multiply both sides by 4/11 to isolate x:
x = (14 * 4) / 11
x = 56 / 11
x = 5.09 (rounded to two decimal places)
Step 4: Substitute the value of x back into the first equation to solve for y.
y = 3 + (1/4)(5.09)
y = 3 + 1.27
y = 4.27 (rounded to two decimal places)
Hence, the solution to the system of equations is x = 5.09 and y = 4.27.