Solve by substitution method
3x+8y=17
2x+y=14
please show step by step so i can understand better. I keep getting it wrong at the end.
Subtract 2x from both sides of 2x+y=14.
y = 14-2x
3x+8y=17
Substitute 14-2x for y in second equation and solve for x. Insert that value into the first equation and solve for y. Check by inserting both values into the second equation.
hi
To solve the system of equations using the substitution method, follow these steps:
Step 1: Choose one equation to solve for one variable in terms of the other variable. Let's solve the second equation for y in terms of x:
2x + y = 14
subtracting 2x from both sides,
y = 14 - 2x
Step 2: Substitute the expression for y obtained in Step 1 into the other equation. Take the first equation:
3x + 8y = 17
Replace y with 14 - 2x (from Step 1):
3x + 8(14 - 2x) = 17
Step 3: Simplify and solve for x:
Distribute 8 to the terms inside the parentheses:
3x + 112 - 16x = 17
Combine like terms:
-13x + 112 = 17
Subtract 112 from both sides:
-13x = 17 - 112
-13x = -95
Divide both sides by -13:
x = -95 / -13
x = 7.3077 (rounded to four decimal places)
Step 4: Substitute the value of x into either of the original equations to find the value of y. Let's use the second equation:
2x + y = 14
Substitute x = 7.3077:
2(7.3077) + y = 14
Multiply:
14.6154 + y = 14
Subtract 14.6154 from both sides:
y = 14 - 14.6154
y = -0.6154 (rounded to four decimal places)
Therefore, the solution to the system of equations is x = 7.3077 and y = -0.6154.