Answer:
x = -3
y = -2
Step-by-step explanation:
We were given the following information:
Jeanette is thinking of two numbers
Let the 2 numbers be represented by ''x'' & ''y''
Adding 5 times the first number and 2 times the second number gives a total of -19.
Adding 3 times the first number and 2 times the second number gives -13
We will use this information to develop the equations below represented as:
We will proceed to solve for the 2 numbers as shown below:
![\begin{gathered} 5x+2y=-19---------1 \\ 3x+2y=-13---------2 \\ \text{Using elimination method, we will eliminate the variable ''y'' by subtracting equation 2 from 1, as seen below:} \\ 5x-3x+2y-2y=-19-(-13) \\ 2x=-6 \\ \text{Divide both sides by ''2'' to obtain the value of ''x'', we have:} \\ x=-(6)/(2) \\ x=-3 \\ \text{Substitute the value of ''x'' into equation 1 to obtain ''y'', we have:} \\ 5x+2y=-19 \\ 5(-3)+2y=-19 \\ -15+2y=-19 \\ \text{Add ''15'' to both sides, we have:} \\ 2y=-19+15 \\ 2y=-4 \\ \text{Divide both sides by ''2'' to obtain the value of ''x'', we have:} \\ y=-(4)/(2) \\ y=-2 \\ \\ \therefore x=-3,y=-2 \end{gathered}]()
x = -3
y = -2