Answer:
x = 6, y = -113
Step-by-step explanation:
10x - y = 53 --- Equation 1
y = [tex]\frac{-13x+92}{2}[/tex] --- Equation 2
I will be using the substitution method.
Substitute y = [tex]\frac{-13x+92}{2}[/tex] into Equation 1:
10x - y = 53
10x - ([tex]\frac{-13x+92}{2}[/tex]) = 53
I want to make the denominators on the left side of the equation the same, so I will multiply 10x by 2 so that I can get a fraction.
[tex]\frac{20x}{2}[/tex] - ([tex]\frac{-13x+92}{2}[/tex]) = 53
Now that their denominators are both 2, I can combine the numerators under the same denominator.
[tex]\frac{20x-(-13x+92)}{2}[/tex] = 53
Two minuses, one outside a bracket and one inside makes a plus. One plus and one minus make a minus.
[tex]\frac{20x+13x-92}{2}[/tex] = 53
Evaluate like terms.
[tex]\frac{33x-92}{2}[/tex] = 53
Shift the (÷2) over to the right side and turn into (×2).
33x - 92 = 53 × 2
= 106
Shift the (-92) over to the right side and turn into (+92).
33x = 106 + 92
= 198
Find x.
x = 198 ÷ 33
x = 6
Substitute x = 6 into Equation 1:
10x - y = 53
10(-6) - y = 53
Evaluate.
-60 - y = 53
Shift the (-60) over to the right side and turn into (+60).
-y = 53 + 60
= 113
Find y.
y = -113
