Answer:
[tex]x=\frac{7}{5}[/tex]
[tex]y=-\frac{22}{5}[/tex]
Step-by-step explanation:
Given:
The given expressions are.
[tex]6x+y=4[/tex]
[tex]x-4y=19[/tex]
We need to find x and y values.
Solution:
Equation 1⇒ [tex]6x+y=4[/tex]
Equation 2⇒ [tex]x-4y=19[/tex]
First solve the equation 1 for y.
[tex]6x+y=4[/tex]
[tex]y = 4-6x[/tex] --------(3)
Substitute [tex]y = 4-6x[/tex] in equation 2.
[tex]x-4(4-6x)=19[/tex]
Simplify.
[tex]x-(4\times 4 - 4\times 6x)=19[/tex]
[tex]x-(16-24x)=19[/tex]
[tex]x-16+24x=19[/tex]
Add 16 both side of the equation.
[tex]25x-16+16=19+16[/tex]
[tex]25x=35[/tex]
[tex]x=\frac{35}{25}[/tex]
Divide Numerator and denominator by 5.
[tex]x=\frac{7}{5}[/tex]
Substitute x value in equation 3 and simplify.
[tex]y=4-6(\frac{7}{5})[/tex]
[tex]y=4-\frac{6\times 7}{5}[/tex]
[tex]y=4-\frac{42}{5}[/tex]
[tex]y=\frac{5\times 4-42}{5}[/tex]
[tex]y=\frac{20-42}{5}[/tex]
[tex]y=-\frac{22}{5}[/tex].
Therefore, the value of [tex]x=\frac{7}{5}[/tex] and [tex]y=-\frac{22}{5}[/tex].
