Answer: D
Step-by-step explanation:
3x + y = 17
x + 2y = 49
The first thing you can do to decide the solutions they have , is by converting the equations into slope intercept forms.
3x + y = 17 Subtract 3x from both sides
-3x -3x
y = -3x + 17
x + 2y = 49 Subtract x from both sides
-x -x
2y = -x + 49 Divide both sides by 2
y = -1/2x + 49/2
Compare the two equations
y = -3x + 17
y = -1/2x +49/2
Since both equations have different slopes and different y intercepts, then the y will have one solution .
Use the substitution method to solve for x by setting both equations equal each other and solve for x.
-3x + 17 = -1/2x + 49/2 Add 1/2x to both sides
+1/2x +1/2x
-2.5x + 17 = 24.5 Now subtract 17 from both sides
-17 -17
-2.5x = 7.5 Divide both sides by -2.5
x = -3
Now since we know the value of x , input it into one of the equations to solve for y.
y = -3x + 17
y = -3(-3) + 17
y = 9 + 17
y = 26
This means it has only one solution and the solution is (-3,26)
