Question

What is the solution to this system of equations? 10x-y=53 and y= -13x+92/2

Answer 1

Answer:

$x = \frac{99}{23}$ and $y = \frac{-229}{23}$

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

$\frac{23x}{23} = \frac{99}{23}$

$x = \frac{99}{23}$

Recall that y = -13x + 46;

Substitute $\frac{99}{23}$ for x in the above expression

y = -13x + 46 becomes

$y = -13*\frac{99}{23} + 46$

$y = \frac{-1287}{23} + 46$

Take LCM

$y = \frac{-1287+1058}{23}$

$y = \frac{-229}{23}$

The solution to the above set of equation is $x = \frac{99}{23}$ and $y = \frac{-229}{23}$