How do you solve the linear equations
x+y=5
3x-y=3
by use of the Substitution Method?
(Please do not confuse with the Elimination Method)
In the top equation, x=-y+5
put that in the bottom equation..
3(-y+5)+y=5
solve for y.
b2+14b+49
To solve the given system of linear equations using the Substitution Method, follow these steps:
1. Start by solving one equation for one variable in terms of the other variable. Let's solve the first equation for x.
x + y = 5
Subtract y from both sides:
x = 5 - y
2. Now we have an expression for x in terms of y. Substitute this expression into the second equation for x.
3x - y = 3
Substituting x = 5 - y:
3(5 - y) - y = 3
3. Simplify the equation by distributing 3 to both terms inside the parentheses:
15 - 3y - y = 3
4. Combine like terms by adding and subtracting y terms:
15 - 4y = 3
5. Isolate the variable by subtracting 15 from both sides:
-4y = 3 - 15
-4y = -12
6. Divide both sides by -4 to solve for y:
y = (-12) / (-4)
y = 3
7. Now that we have the value of y, substitute it back into either of the original equations to solve for x. Let's use the first equation:
x + y = 5
Substituting y = 3:
x + 3 = 5
8. Subtract 3 from both sides:
x = 5 - 3
x = 2
9. The solution to the system of linear equations is x = 2 and y = 3.
So, by using the Substitution Method, we found the solution x = 2 and y = 3 for the given linear equations.