Using a graph to solve the system of linear equations of x+y=5 and y−2x=−4

Answer 1

"Use a graph to solve" means you gotta draw 'em!

Method 1: solve for x = 0 and y = 0 (i.e. the y axis and x axis respectively):

x + y = 5

set x = 0 then 0 + y = 5 => y = 5 so lines passes through (0, 5)

set y = 0 then x + 0 = 5 => x = 5 so line passes through (5,0)

plot both points, draw a straight line passing through them

y - 2x = -4

if x = 0 then y = -4 so line passes through (0, -4)

if y = 0 then x = 2 so line passes through (2,0)

plot both points, draw a straight line passing through them

Method 2: using slope intercept form.

First step is rearranging each equation in slope-intercept form y = mx + b.

m = gradient = change in y / change in x, and b = y intercept

x + y = 5 becomes y = -x + 5

gradient = -1 (1 down, 1 across) and passes through (0, b) or (0,5)

you can now plot the point (0,5) and mark a second point e.g. (1, 4)

draw a straight line passing through them

y - 2x = -4 becomes y = 2x - 4

gradient = 2 (4 up, 2 across) and passes through (0, b) or (0, -4)

plot the point (0, -4) and mark a second point based on the gradient e.g. (2, 0)

draw a straight line passing through them

Solve

Once you have drawn both lines, find the "solution". This is the point where the two lines intersect.

Mathematically, it is where the two functions are equal, so (do this if the question asks you to "solve", "find", etc.):

if y = -x + 5 and y = 2x - 4 we can say that therefore -x + 5 = 2x - 4

=> 3x = 9 => x = 3

now we have x, plug into either of the equations to get y = 2(3) - 4 = 2

hence point of intersection or solution is (3,2)