Find solutions to your problems with the help of IDNLearn.com's expert community. Discover detailed answers to your questions with our extensive database of expert knowledge.
Sagot :
GIVEN:
We are given the following system of eequations;
[tex]\begin{gathered} 5x+9y=15---(1) \\ \\ x+2y=5----(2) \end{gathered}[/tex]Required;
To solve the system of equations and enter exact answer as an ordered pair (x,y).
Step-by-step solution;
To solve these equations, we first of all take note that one of the unknowns has a coefficient of 1. That is x in equation (2).
Hence, taking equation (2), make x the subject of the equation and we'll have;
[tex]x=5-2y[/tex]Now we substitute the value of x into equation (1), as follows;
[tex]\begin{gathered} 5x+9y=15 \\ \\ Where;\text{ }x=5-2y \\ \\ 5(5-2y)+9y=15 \\ \\ 25-10y+9y=15 \\ \\ 25-y=15 \\ \\ Subtract\text{ }25\text{ }from\text{ }both\text{ }sides; \\ \\ -y=-10 \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }-1; \\ \\ \frac{-y}{-1}=\frac{-10}{-1} \\ \\ y=10 \end{gathered}[/tex]We now have the vaalue of y.
We will substitute this value into either of the equations to get the value of x.
Substitute for y = 10 into equation (2);
[tex]\begin{gathered} x+2y=5 \\ \\ x+2(10)=5 \\ \\ x+20=5 \\ \\ Subtract\text{ }20\text{ }from\text{ }both\text{ }sides; \\ \\ x=-15 \end{gathered}[/tex]Therefore,
ANSWER:
The answer as an ordered pair will be;
[tex](-15,10)[/tex]
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com is your reliable source for answers. We appreciate your visit and look forward to assisting you again soon.
