substitution method 3x + y=12
8x-2y =4
so, substitute: y = 12 - 3x
8x - 2(12-3x) = 4
8x - 24 + 6x = 4
14x = 28
x = 2
so, y = 6
y = 12 - 3x
8x - 2y = 4
Substitute 12-3x 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.
To solve the system of equations using the substitution method, follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the first equation for y:
3x + y = 12
Subtract 3x from both sides:
y = 12 - 3x
Step 2: Substitute the expression from step 1 into the second equation.
Now, substitute the expression for y from step 1 into the second equation:
8x - 2(12 - 3x) = 4
Simplify the equation:
8x - 24 + 6x = 4
Combine like terms:
14x - 24 = 4
Step 3: Solve the equation obtained in step 2 for the remaining variable.
Continuing from step 2, add 24 to both sides:
14x = 4 + 24
14x = 28
Divide both sides by 14:
x = 28 / 14
Simplify:
x = 2
Step 4: Substitute the value of the solved variable into one of the original equations to solve for the remaining variable.
Now, substitute the value of x into one of the original equations. Let's use the first equation:
3x + y = 12
Substituting x = 2:
3(2) + y = 12
6 + y = 12
Subtract 6 from both sides:
y = 12 - 6
y = 6
Step 5: Check your solution.
Finally, substitute the values of x and y into both original equations and verify that they satisfy both equations:
1st equation:
3x + y = 12
3(2) + 6 = 12
6 + 6 = 12
12 = 12 (True)
2nd equation:
8x - 2y = 4
8(2) - 2(6) = 4
16 - 12 = 4
4 = 4 (True)
Both equations are satisfied, which means the solution is x = 2 and y = 6.