Answer:
Step-by-step explanation:
1. Find the system for 2x+3y=5 and 3x+y=6 using substition.
I will solve your system by substitution.
(You can also solve this system by elimination.)
3x+y=6;2x+3y=5
Step: Solve3x+y=6for y:
3x+y+−3x=6+−3x(Add -3x to both sides)
y=−3x+6
Step: Substitute−3x+6foryin2x+3y=5:
2x+3y=5
2x+3(−3x+6)=5
−7x+18=5(Simplify both sides of the equation)
−7x+18+−18=5+−18(Add -18 to both sides)
−7x=−13 (Divide both sides by -7)
x=[tex]\frac{13}{7}[/tex]
Step: Substitute [tex]\frac{13}{7}[/tex] forxiny=−3x+6
y=−3x+6
y=−3([tex]\frac{13}{7}[/tex])+6
y=[tex]\frac{3}{7}[/tex]
2. Let's solve your system by elimination.
3x+y=6;2x+3y=5
Multiply the first equation by -3,and multiply the second equation by 1.
−3(3x+y=6)
1(2x+3y=5)
Becomes:
−9x−3y=−18
2x+3y=5
Add these equations to eliminate y:
−7x=−13
Then solve−7x=−13for x:
−7x=−13 (Divide both sides by -7)
x=[tex]\frac{13}{7}[/tex]
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
3x+y=6
Substitute[tex]\frac{13}{7}[/tex] forxin3x+y=6
3([tex]\frac{13}{7}[/tex])=6 (Simplify both sides of the equation)
y+39/7+−39/7=6+−39/7 (Add (-39)/7 to both sides)
y=[tex]\frac{3}{7}[/tex]
