Answer:
A. (3,2)
Step-by-step explanation:
One way to solve without graphing
equate both equations to each other:
[tex]2x - 4 = - x + 5[/tex]
add x on both sides:
[tex]2x + x - 4 = 5[/tex]
add 4 on both sides:
[tex]2x + x = 5 + 4[/tex]
collect like terms:
[tex]3x = 9[/tex]
divide 3 on both sides, so
[tex]x = 3[/tex]
now that we have x, go back to any one of the equations and substitute x=3 to find y. I'll use y=2x-4
[tex]y = 2x - 4[/tex]
sub x=3
[tex]y = 2(3) - 4[/tex]
2 × 3 is 6
[tex]y = 6 - 4[/tex]
[tex]y = 2[/tex]
we now have x and y, so the coordinates are (3,2)
If you want to use the graphing method, substitute in x values of your choice, for example -2 to 2 into each equation to find y and when there is a same coordinate in both equations that is the solution.
y = 2x - 4
when x is -2, y = 2(-2)-4 = -8. (-2,-8)
when x is -1, y = 2(-1) - 4= -6. (-1,-6)
when x is 0, y = 2(0)-4 = -4. (0,-4)
when x is 1, y = 2(1) - 4 = -2. (1,-2)
when x is 2, y = 2(2) - 4 = 0. (2,0)
when x is 3, y = 2(3) - 4 = 2. (3,2)
do the same thing of substituting to the other equation
y = -x + 5
when x is -2, y is 7 (-2,7)
when x is -1, y is 6. (-1,6)
when x is 0, y is 5. (0,5)
when x is 1, y is 4. (1,4)
when x is 2, y is 3. (2,3)
when x is 3, y is 2. (3,2)
plot these coordinates on a graph
they both have same x value (3) and same y value (2)
