Answer:
([tex]\frac{9}{4},\frac{1}{4})[/tex]
Step-by-step explanation:
We are given that two lines
[tex]x_1-7x_2=5[/tex] and [tex]x_1-5x_2=1[/tex]
We have to find the intersection point of two lines
Let [tex]3x_1-7x_2=5[/tex] (equation 1)
[tex]x_1-5x_2=1[/tex] (Equation 2)
Multiply equation 2 by 3 then subtract from equation 1
[tex]-7x_2+15x_2=5-3[/tex]
[tex]8x_2=2[/tex]
[tex]x_2=\frac{2}{8}=\frac{1}{4}[/tex]
Substitute [tex] x_2=\frac{1}{4}[/tex] in the equation 1
Then, we get
[tex]3x_1-7\frac{1}{4}=5[/tex]
[tex]3x_1-\frac{7}{4}=5[/tex]
[tex]3x_1=5+\frac{7}{4}=\frac{20+7}{4}=\frac{27}{4}[/tex]
[tex]x_1=\frac{27}{4\times 3}=\frac{9}{4}[/tex]
Hence, the intersection point of two given lines is ([tex]\frac{9}{4},\frac{1}{4})[/tex]
