Respuesta :
Answer: x = 4, y = 3
Step-by-step explanation:
[tex]y=\dfrac{1}{4}x+2[/tex] and [tex]y=x-1[/tex]
Using substitution method we get:
[tex]x-1=\dfrac{1}{4}x+2\\\\\text{subtract}\ \dfrac{1}{4}x\ \text{from both sides}\rightarrow \dfrac{3}{4}x-1=2\\\\\text{add 1 to both sides}\rightarrow \dfrac{3}{4}x=3\\\\\text{multiply both sides by 4}\rightarrow 3x=12\\\\\text{divide both sides by 3}\rightarrow x=4\\\\\text{Insert x = 4 into one of the original equations to solve for y:}\\y=x-1\\y =(4)-1\\y=3[/tex]
Ordered pair of solution of the system of a linear equation is the value of its variables. Ordered pair of given equations is (4, 3)
What is system of linear equation?
A system of linear equation is the set of equation with highest power of variable equal to one. In system of linear equation is the finite set of equation present for which the common solution is sought.
Given information-
The first equation given in the problem is,
[tex]y=\dfrac{1}{4}x+2[/tex]
The second equation given in the problem is,
[tex]y=x-1[/tex]
Solve the given equation using the substitution method to find out the ordered pair.
The second equation given in the problem is,
[tex]y=x-1[/tex]
Put the value of y from the first equation into the above equation as,
[tex]\dfrac{1}{4}x+2=x-1\\x-\dfrac{1}{4}x=2+1\\\dfrac{4-1}{4}x=3\\\dfrac{3}{4}x=3\\x=4[/tex]
Thus the value of x is 4. Put this value in the second equation as,
[tex]y=4-1\\y=3[/tex]
Thus the value of y is 3.
Hence, ordered pair for the solution of the system of a linear equation given is (4, 3).
Learn more about the system of equations here;
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