3x =2y = 17
2x-y =9
and
3x+y = 3
x+2y = -4
How do I do these??
22Z 6Y
These are simultaneous equations. You have a typo in #1.
For the second set, just multiply equation 1 by 2, then subtract equation 2 from equation 1 (which will eliminate y), then solve for x. Post your work if you get stuck and need further assistance.
These are simultaneous equations. You have a typo in #1.
For the second set, just multiply equation 1 by 2, then subtract equation 2 from equation 1 (which will eliminate y), then solve for x. Post your work if you get stuck and need further assistance.
To solve simultaneous equations, we can use different methods such as substitution, elimination, or graphical representation. Let's solve the second set of equations using the elimination method:
Step 1: Multiply equation 1 by 3 and equation 2 by -2 to make the coefficients of y in both equations equal:
(3x + y) * 3 = 3 * 3
(x + 2y) * -2 = -4 * -2
Which simplifies to:
9x + 3y = 9
-2x - 4y = 8
Step 2: Multiply equation 2 by -2 to make the coefficients of x in both equations equal:
-2 * (-2x - 4y) = -2 * 8
Which simplifies to:
4x + 8y = -16
Now, we have the equations:
9x + 3y = 9
4x + 8y = -16
Step 3: Multiply equation 1 by -4:
-4 * (9x + 3y) = -4 * 9
Which simplifies to:
-36x - 12y = -36
Now, we have the equations:
-36x - 12y = -36
4x + 8y = -16
Step 4: Add the equations together:
(-36x - 12y) + (4x + 8y) = (-36) + (-16)
Which simplifies to:
-32x - 4y = -52
Now, we have the equations:
-32x - 4y = -52
4x + 8y = -16
Step 5: Solve for x by multiplying equation 2 by 8:
8 * (4x + 8y) = 8 * (-16)
Which simplifies to:
32x + 64y = -128
Now, we have the equations:
-32x - 4y = -52
32x + 64y = -128
Step 6: Add the equations together:
(-32x - 4y) + (32x + 64y) = (-52) + (-128)
Which simplifies to:
60y = -180
Step 7: Solve for y:
y = -180 / 60
y = -3
Step 8: Substitute the value of y back into one of the original equations to solve for x. Let's use equation 1:
3x + (-3) = 3
Which simplifies to:
3x - 3 = 3
Step 9: Solve for x:
3x = 3 + 3
3x = 6
x = 2
So, the solution to the second set of equations is x = 2 and y = -3.