MATH SOLVE

3 months ago

Q:
# solve the system of linier equations by A) Substitution, B) elimination

Accepted Solution

A:

[tex]5x + y = 10 \\ 2x - 6y = 4[/tex]

let's start with substitution. we will solve for one variable using one equation and then substitute j to the other equation. for example let's take the first equation and solve for y

[tex]y = 10 - 5x[/tex]

now put this I to second formula

[tex]2x - 6(10 - 5x) = 4 \\ 2x - 60 + 30x = 4 \\ 32x = 64 \\ x = 2[/tex]

now put this back into first equation

[tex]5(2) + y = 10 \\ 10 + y = 10 \\ y = 0[/tex]

so we get x is 2 and y is 0

now we will save using elimination. to do this we wi multiply one equation so that we can add both equations and cancel out a variable

we will multiply the first equation. by 6

[tex]6(5x + y = 10) \\ 30x + 6y = 60[/tex]

now we will add the two equations

[tex] 30x + 6y = 60\\ + 2x - 6y = 4 \\ 32x = 64 \\ x = 2[/tex]

you can do the same thing and cancel out x to find y.

[tex]5x + y = 10 \\ 2x - 6y = 4[/tex]

let's start with substitution. we will solve for one variable using one equation and then substitute j to the other equation. for example let's take the first equation and solve for y

[tex]y = 10 - 5x[/tex]

now put this I to second formula

[tex]2x - 6(10 - 5x) = 4 \\ 2x - 60 + 30x = 4 \\ 32x = 64 \\ x = 2[/tex]

now put this back into first equation

[tex]5(2) + y = 10 \\ 10 + y = 10 \\ y = 0[/tex]

so we get x is 2 and y is 0

now we will save using elimination. to do this we wi multiply one equation so that we can add both equations and cancel out a variable

we will multiply the first equation. by 6

[tex]6(5x + y = 10) \\ 30x + 6y = 60[/tex]

now we will add the two equations

[tex] 30x + 6y = 60\\ + 2x - 6y = 4 \\ 32x = 64 \\ x = 2[/tex]

you can do the same thing and cancel out x to find y.