X-2y=5 2x-4y=10
Put both equations in slope-intercept form
Solve the systems of equations by substitution
Solve the systems of equations by graphing
ONE HUNDRED POINTS HURRY
Answers
Step-by-step explanation:
X-2y=5 ; 2x-4y=10
• x - 2y = 5 • 2x -4y = 10
-2y = -x+5 -4y= -2x +10
y1 = ½x - 5/2 y2 = ½x -5/2
• => y1 = y2
½x -5/2 = ½x -5/2
the systems have no solution
• graph as attached
Answer:
[tex]\textsf{Equation 1}: \quad y=\dfrac{1}{2}x-\dfrac{5}{2}[/tex]
[tex]\textsf{Equation 2}: \quad y=\dfrac{1}{2}x-\dfrac{5}{2}[/tex]
True for all x (infinitely many solutions)
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]y = mx + b[/tex]
(where m is the slope and b is the y-intercept)
Given equations:
[tex]\begin{cases}x-2y=5\\2x-4y=10\end{cases}[/tex]
To put both equations in slope-intercept form, rearrange both equations to make y the subject:
Equation 1
[tex]\implies x-2y=5[/tex]
[tex]\implies x-2y+2y=5+2y[/tex]
[tex]\implies x=5+2y[/tex]
[tex]\implies x-5=5+2y-5[/tex]
[tex]\implies 2y=x-5[/tex]
[tex]\implies 2y \div 2=(x-5) \div 2[/tex]
[tex]\implies y=\dfrac{1}{2}x-\dfrac{5}{2}[/tex]
Equation 2
[tex]\implies 2x-4y=10[/tex]
[tex]\implies 2x-4y+4y=10+4y[/tex]
[tex]\implies 2x=10+4y[/tex]
[tex]\implies 2x-10=10+4y-10[/tex]
[tex]\implies 4y=2x-10[/tex]
[tex]\implies 4y \div 4=(2x-10) \div 4[/tex]
[tex]\implies y=\dfrac{1}{2}x-\dfrac{5}{2}[/tex]
Therefore, both equations are the same as they have the same slope and y-intercept.
As both equations are the same, this system of equations is called an equivalent system.
To solve a system of equations by substitution, substitute one equation into the other:
[tex]\implies \dfrac{1}{2}x-\dfrac{5}{2}= \dfrac{1}{2}x-\dfrac{5}{2}[/tex]
As both sides are equal, the solution is true for all x.
The solution to a graphed system of equations is the point(s) of intersection.
When graphing the given system of equations, as the lines are the same, they will be on top of each other. They are called coincident lines and have infinitely many solutions since the lines have the same slope and same y-intercept.
Learn more about systems of equations here:
https://brainly.com/question/21447811
https://brainly.com/question/27357423
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