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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]
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