SOLVE BY SUBSTITUTION
3.) x=4 y=20
Step-by-step:
Substitute into one of the equations
[tex]x+5x=24[/tex]
Combine like terms
[tex]6x=24\\[/tex]
Divide both sides of the equation by the coefficient of variable
[tex]x=\frac{24}{6}[/tex]
Cross out the common factor
[tex]x=4[/tex]
[tex]\left \{ {{x+y=24} \atop {x=4}} \right.[/tex]
Substitute into one of the equations
[tex]4+y=24[/tex]
Rearrange unknown terms to the left side of the equation
[tex]y=24-4[/tex]
Calculate sum of the difference
[tex]y=20[/tex]
therefore the answer is: [tex]x=4 ,y=20[/tex]
4. x=12 , y=9
Solving steps:
[tex]3x-4y=0,2x+y=33[/tex]
Multiply both sides of the equation by a coefficient
[tex]3x-4y=0\\4(2x+y)=33x4[/tex]
Same solutions with number 1
SOLVE BY ELIMINATION METHOD
5.) x=1 and y=2
Let's solve your system by elimination.
- 3x+2y=7;5x−2y=1
- 3x+2y=7
- 5x−2y=1
Add these equations to eliminate y:
Then solve 8x=8 for x:
- 8x=88
- [tex]\frac{8x}{8}=\frac{8}{8}[/tex] (Divide both sides by 8)
- x=1
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
- 3x+2y=7
Substitute 1 for x in 3x+2y=7:
- (3)(1)+2y=7
- 2y+3=7(Simplify both sides of the equation)
- 2y+3+−3=7+−3(Add -3 to both sides)
- 2y=4
- [tex]\frac{2y}{2} =\frac{4}{2}[/tex] (Divide both sides by 2)
- y=2
6.) a=5 and b=4
Let's solve your system by elimination.
Add these equations to eliminate b:
Then solve2a=10for a:
[tex]\frac{2a}{2} =\frac{10}{2}[/tex] (Divide both sides by 2)
a=5
Now that we've found a let's plug it back in to solve for b.
Write down an original equation:
Substitute 5 for a in a+b=9:
- 5 +b=9
- b+5=9(Simplify both sides of the equation)
- b+5+-5=9+-5 (Add -5 to both sides)
- b=4
