Graphing the two given equations, let's first determine their x and y intercepts to easily plot them.
2x + y = 4
At x = 0, At y = 0,
2(0) + y = 4 2x + (0) = 4
0 + y = 4 2x + 0 = 4
y = 4 2x = 4
(0,4) 2x/2 = 4/2
x = 2
(2,0)
y - 2x = 6
At x = 0, At y = 0,
y - 2(0) = 6 (0) - 2x = 6
y - 0 = 6 -2x = 6
y = 6 -2x/-2 = 6/-2
(0,6) x = -3
(-3,0)
Let's now plot the graphs,
It appears that the two graphs intersect at (-1/2, 5). The point of intersection is also the solution.
Let's check using the Substitution Method:
2x + y = 4 (Equation 1)
y - 2x = 6 (Equation 2)
y - 2x = 6
y = 2x + 6 (Substitute to Equation 1)
2x + y = 4
2x + (2x + 6) = 4
2x + 2x + 6 = 4
4x = 4 - 6
4x = -2
4x/4 = -2/4
x = -1/2 or -0.5
Let's determine y,
y - 2x = 6
y - 2(-1/2) = 6
y + 1 = 6
y = 6 - 1
y = 5
Therefore, the solution is -1/2, 5. The answer is correct.