Answer:
A. The solution is x = 4 and y = 1
Step-by-step Explanation:
Given the below system of equations;
[tex]\begin{gathered} x+y=5\ldots\ldots\text{.}\mathrm{}\text{Equation 1} \\ x-y=3\ldots\ldots\text{.}\mathrm{}\text{Equation 2} \end{gathered}[/tex]
To solve the above system of equations, we'll follow the below steps;
Step 1: Subtract Equation 2 from Equation 1;
[tex]\begin{gathered} (x-x)+(y-(-y))=(5-3) \\ 0+2y=2 \\ y=\frac{2}{2} \\ y=1 \end{gathered}[/tex]
Step 2: Substitute the value of y into Equation 1 and solve for x;
[tex]\begin{gathered} x+1=5 \\ x=5-1 \\ x=4 \end{gathered}[/tex]
The solution is x = 4 and y = 1
If we convert the given equations into slope-intercept form of the equation of a line generally given as;
[tex]y=mx+b[/tex]
where m = slope of the line and b = y-intercept of the line
Converting the two equations, we'll have;
[tex]\begin{gathered} y=-x+5 \\ y=x-3 \end{gathered}[/tex]
We can see that for the 1st equation, slope(m) = -1 and y-intercept(b) = 5 while for the 2nd equation, slope(m) = 1 and y-intercept(b) = -3.
With the above information, we can go ahead and plot the graphs of both lines as seen below;
We can also see from the graph that, at the point of intersection of both lines, x = 4 and y = 1 which is the solution and it aligns with what we had earlier.
