Answer:
For x - y = 2
You need to find x or y in one of the equations and then substitute that into the other.
So we have;
x-y=2
4x-3y=11
We will take the first equation and find x;
x-y=2
add y to both sides;
x-y+y=2+y
x=2+y
Now we take that answer and substitute it forx in the other equation;
4(2+y)-3y=11
8+4y-3y=11
8+y=11
y=3
Now we have what y equals, so we use it in the first equation to find x;
x-3=2
x=5
So we have;
x=5; y=3
Hope you understand!
=)
And for 4x – 3y = 11
Multiply the first equation by 2 and the second by 3 so that there are the same number of y's in each:
8x - 6y = 22 ...(3)
30x + 6y = -3 ...(4)
Now add (3) and (4) term by term:
38x + 0 = 19
or
38x = 19
or x = 1/2
Put this back into equation (1)
4*(1/2) - 3y = 11
or
2 - 3y = 11
Subtract 2 from both sides:
-3y = 9
Divide both sides by -3
y = -3
Answer:
The answer is one solution, the lines intersect at point (5,3)
Step-by-step explanation:
The method I used to solve this is substitution.
1. First I solved for x in the equation 4x – 3y = 11. Which is x = [tex]\frac{3y+11}{4}[/tex]
2. Second solved for y in the equation x - y = 2. Which is y = x-2
3. Then substitute the y in the equation x = [tex]\frac{3y+11}{4}[/tex] for y = x-2 to find the value of x. Which is x = 5
4. Lastly plug in 5 for x in the equation y = x-2. Which is three
The answer is one solution, the lines intersect at point (5,3)
Explanation for each step.
1. 4x - 3y = 11
+3y (add 3y to both sides of equation.)
4x = (3y + 11 )/4 divide both sides by 4, to get x alone
x = [tex]\frac{3y+11}{4}[/tex]
2. x - y = 2.
+ y (add y to both sides of equation.
x = y +2
3. x = [tex]\frac{3y+11}{4}[/tex]
= [tex]\frac{3(x-2)+11}{4}[/tex] (substitute)
= [tex]\frac{3x -6 + 11}{4}[/tex] (add -6 and 11)
4(x) = ([tex]\frac{3x + 5}{4}[/tex])4 multiply both side by 4
4x = 3x + 5
-3x subtract -3x
x = 5
4. y = x-2
= 5 - 2 substitute
y = 3
Side note: this took waaaay too long to complete, yet i hope this helped :)
