Answer:
1) x = 3, y = 2 or (3, 2)
2) x = 0, y = 2 or (0, 2)
6) x = 3, y = – 4 or (3, – 4)
Step-by-step explanation:
I will only provide solutions for questions 1, 3, and 6 in accordance with Brainly's guidelines.
Question 1:
[tex]\displaystyle\mathsf{\left \{ {{\:\:Equation\:1:\:y\:=\:-2x\:+\:5} \atop{Equation\:2:\:y\:=\:-x\:+\:2}} \right. }[/tex]
Substitute the value of y in equation 2 into the first equation:
y = -2x + 5
-x + 2 = -2x + 5
Add 2x on both sides:
-x + 2x + 2 = -2x + 2x + 5
x + 2 = 5
Subtract 2 from both sides to isolate x:
x + 2 - 2 = 5 - 2
x = 3
Substitute the value of x into Equation 2 to solve for the value of y:
y = -x + 5
y = -(3) + 5
y = 2
Solution of the given systems of linear equations:
Therefore, the solution to the given systems of linear equations is: x = 3, y = 2 or (3, 2).
Question 3:
[tex]\displaystyle\mathsf{\left \{ {{Equation\:1:\:3x\:+\:5y=\:10} \atop{Equation\:2:\:y\:=\:-5x\:+\:2}} \right. }[/tex]
Substitute the value of y from Equation 2 into Equation 1:
3x + 5y = 10
3x + 5(-5x + 2) = 10
Distribute 5 into the parenthesis:
3x + -25x + 10 = 10
Combine like terms:
-22x + 10 = 10
Subtract 10 from both sides:
-22x + 10 - 10 = 10 - 10
-22x = 0
Divide both sides by -22 to solve for x:
[tex]\displaystyle\mathsf{\frac{-22x}{-22}\:=\:\frac{0}{-22}}[/tex]
x = 0
Substiute the value of x into Equation 2 to solve for y:
y = -5x + 2
y = -5(0) + 2
y = 2
Solution of the given systems of linear equations:
Therefore, the solution to the given systems of linear equations is: x = 0, y = 2 or (0, 2).
Question 6:
[tex]\displaystyle\mathsf{\left \{\quad\:Equation\:1:\:-2x+6y=\:-30} \atop{Equation\:2:\:y-2x=\:-10}} \right.}[/tex]
Add 2x to both sides of Equation 2 to isolate y:
y – 2x = –10
y – 2x + 2x = 2x – 10
y = 2x – 10
Substitute the value of y from the previous step into Equation 1:
– 2x + 6y = – 30
– 2x + 6(2x – 10) = – 30
Distribute 6 into the parenthesis:
– 2x + 12x – 60 = – 30
Combine like terms:
10x – 60 = – 30
Add 60 to both sides:
10x – 60 + 60 = – 30 + 60
10x = 30
[tex]\displaystyle\mathsf{\frac{10x}{10}\:=\:\frac{30}{10} }[/tex]
x = 3
Substitute the value of x into Equation 2 to solve for y:
y – 2x = –10
y – 2(3) = –10
y – 6 = –10
y – 6 + 6 = –10 + 6
y = – 4
Solution of the given systems of linear equations:
Therefore, the solution to the given systems of linear equations is: x = 3, y = – 4 or (3, – 4).
