Answer:
[tex]x=\frac{15}{22}[/tex]
[tex]y=\frac{27}{11}[/tex]
Step-by-step explanation:
Given system of equations:
A) [tex]8x-y=3[/tex]
B) [tex]4x+5y=15[/tex]
To solve for [tex]x[/tex] and [tex]y[/tex]
Using substitution method to solve the system.
Rearranging equation A, to solve for [tex]y[/tex] in terms of [tex]x[/tex]
Subtracting both sides by [tex]3[/tex]
[tex]8x-y-3=3-3[/tex]
[tex]8x-y-3=0[/tex]
Adding [tex]y[/tex] both sides.
[tex]8x-y+y-3=0+y[/tex]
[tex]8x-3=y[/tex]
So, we have [tex]y=8x-3[/tex]
Substituting value of [tex]y[/tex] we got from A into equation B.
[tex]4x+5(8x-3)=15[/tex]
Using distribution.
[tex]4x+40x-15=15[/tex]
Simplifying.
[tex]44x-15=15[/tex]
Adding 15 both sides.
[tex]44x-15+15=15+15[/tex]
[tex]44x=30[/tex]
Dividing both sides by 44.
[tex]\frac{44x}{44}=\frac{30}{44}[/tex]
Simplifying fractions.
∴ [tex]x=\frac{15}{22}[/tex] (Answer)
We can plugin [tex]x=\frac{15}{22}[/tex] in the rearranged equation A to get value of [tex]y[/tex]
[tex]y=8(\frac{15}{22})-3[/tex]
[tex]y=\frac{120}{22}-3[/tex]
Simplifying fractions.
[tex]y=\frac{60}{11}-3[/tex]
Making whole numbers to fractions.
[tex]y=\frac{60}{11}-\frac{3}{1}[/tex]
Taking LCD = 11 to subtract fractions
[tex]y=\frac{60}{11}-\frac{33}{11}[/tex]
[tex]y=\frac{60-33}{11}[/tex]
∴ [tex]y=\frac{27}{11}[/tex] (Answer)
