Question

5x+9y=15x+2y=5 solve system of equationsenter exact answer as an ordered pair(x,y

Answer 1

GIVEN:

We are given the following system of eequations;

`\begin{gathered} 5x+9y=15---(1) \\ \\ x+2y=5----(2) \end{gathered}`

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;

`x=5-2y`

Now we substitute the value of x into equation (1), as follows;

`\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; \\ \\ (-y)/(-1)=(-10)/(-1) \\ \\ y=10 \end{gathered}`

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);

`\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}`

Therefore,

ANSWER:

The answer as an ordered pair will be;

`(-15,10)`