Answer :
I like to work with the slope-intercept form of the line:
x=4y-8 �> y = (1/4)x + 2 (1)
12x+y=11 �> y = -12x + 11 (2)
At the point where they intersect the two y values must be equal, so set eq(1) = eq(2):
(1/4)x + 2 = -12x + 11
( (1/4) + (48/4))x = 9
(49/4)x = 9
Ans: x = 36/49
Check: Plug in x=36/49 to eq(1) and eq(2) to make sure they produce identical y values:
(1) y = (1/4)(36/49) + 2 = (9/49) + (98/49) = 107/49
(2) y = -12(36/49) + 11 = (-432/49) + (539/49) = 107/49 (they match)
By using substitution method,
The x-coordinate of the point where the lines x=4y−8 and 12x+y=11 intersect is [tex]\frac{36}{49}[/tex].
What is substitution method?
"The substitution method is one of the algebraic methods to solve linear equations. It involves substituting the value of any one of the variables from one equation to the other equation."
We have the lines
x=4y−8 ..........................(1)
12x+y=11 .........................(2)
By using substitution method
Substitute x = 4y - 8 in equation (2)
⇒ 12(4y-8) + y = 11
⇒ 48y - 96 + y = 11
⇒ 49y = 11 + 96
⇒ y = [tex]\frac{107}{49}[/tex]
Calculating the x - coordinate by substituting y value in equation (1)
x=4y−8
⇒ x = [tex]4(\frac{107}{49} )-8[/tex]
⇒ x = [tex]\frac{428-392}{49}[/tex]
⇒ x = [tex]\frac{36}{49}[/tex]
Hence, the x-coordinate of the point where the lines x=4y−8 and 12x+y=11 intersect is [tex]\frac{36}{49}[/tex].
Learn more about substitution method here
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