Solve the system of 2 linear equations by substitution

Question

Solve the system of 2 linear equations by substitution. Write solution as an ordered pair (x,y)

3x+y=5

2x+3y=8

Answer 1

3x+y=5

2x+3y=8

substitution means we are going to substitute an expression for x or y into one of the equations so there is only one variable , only x in an equation or only y in an equation, and the we can m

1.substitute an expression for x or y into one of the equations

3x+y=5 can be rearranged to read y=-3x+5,

2.now we have an expression for y we can substitute into the second equation 2x+3y=8

2x+3(-3x+5)=8.

3.now we can solve mathematically for x 2x-9x+15=8 -7x=-7 x=1

4.next, solve for y using either equations 3(1)+y=5 y=2

5.next double check your answer by by placing your x and y in either equation

Answer 2

x=1

y=2

Answer 3

3x+y=5

2x+3y=8

Just carefully follow this secret recipe for the easiest and most convenient way of solving this.

1. The easiest way to solve these 2 equations by substitution is to get (y) in terms of (x) from the first equation
2. Now, you will have: y=5-3x.
3. Since you got the expression for y, you can substitute it in the other equation.
4. Now, you have 2x+3(5-3x)=8
5. Now it's so easy, you just distribute the 3 on the bracket next to it: 2x+15-9x=8
6. Then, combine the 2x and 9x: 15-7x=8
7. Get x on one side and the other terms on the other: -7x=-7
8. x=(-7)/(-7)=1
9. Now, since you got the value for x, you can substitute it in any of the original equations to get the value of y.
10. Substitute the value of x: 3(1)+y=5
11. Isolate y: y=5-3(1)=5-3=2

Answer 4

Solving system of 2 equations by substitution (detailed solution!!)