Answer:
[tex]x = \frac{99}{23}[/tex] and [tex]y = \frac{-229}{23}[/tex]
Step-by-step explanation:
Given
10x - y = 53
y = -13x + 92/2
Required
Find x and y
The above system of equation represent simultaneous equation.
There are few ways of solving simultaneous equation; one of them is substitution method. We'll make use of the substitution method.
Rewrite equations
10x - y = 53 --------- Equation 1
y = -13x + 92/2 --------- Equation 2
Simplify equation 2
y = -13x + 92/2
y = -13x + 46
Substitute -13x + 46 for y in equation 1
10x - y = 53 becomes
10x - (-13x + 46) = 53
Open the bracket
10x + 13x - 46 = 53
Collect like terms
10x + 13x = 46 + 53
23x = 99
Divide both sides by 23
[tex]\frac{23x}{23} = \frac{99}{23}[/tex]
[tex]x = \frac{99}{23}[/tex]
Recall that y = -13x + 46;
Substitute [tex]\frac{99}{23}[/tex] for x in the above expression
y = -13x + 46 becomes
[tex]y = -13*\frac{99}{23} + 46[/tex]
[tex]y = \frac{-1287}{23} + 46[/tex]
Take LCM
[tex]y = \frac{-1287+1058}{23}[/tex]
[tex]y = \frac{-229}{23}[/tex]
The solution to the above set of equation is [tex]x = \frac{99}{23}[/tex] and [tex]y = \frac{-229}{23}[/tex]
