4x - 3y = 6
-5x + 7y = -1
SHOW WORK SO I CAN ACTUALLY LEARN HOW TO DO IT.
-5x + 7y = -1
SHOW WORK SO I CAN ACTUALLY LEARN HOW TO DO IT.
-
We wish to eliminate some variable. We don't really care which one it is for this problem because both of them are about as hard as one another. So we choose X.
Multiply the first equation by -5. We choose -5 because it is the coefficient of x in the second equation.
The first equation becomes
-20 + 15y = -30
Similarly, and for the same reason, multiply the second equation by 4.
It then becomes
-20x + 28y = -4
Now we will subtract these two equations by subtracting the expressions on the left sides of the equals signs, and then doing the same to the ones on the right sides. It is very important that the order of subtraction is the same for both right and left; that is, if you do [first]-[second] for the left sides, you have to do [first]-[second] again for the right side
In our case, that means
(-20x + 15y) - (-20x + 28y) = (-30) - (-4)
Distribute the negative signs:
-20x + 15y + 20x - 28y = -30 + 4
Combine like terms:
(-20+20)x + (15-28)y = -26
Simplify:
0x - 13y = -26
Simplify:
-13y = -26
Solve for y by dividing both sides by -13:
-13y/-13 = -26/-13
y = 2
Now we have found y.
Thus we can substitute y into any of the original equations. W'll pick the first one because it really doesn't matter which one we use:
4x - 3(2) = 6
Distribute:
4x - 6 = 6
Solve for x by first adding 6 to both sides...
4x - 6 + 6 = 6 + 6
4x = 12
...and then dividing by 4
4x/4 = 12/4
x = 3
Now we have found x.
If you want to be very sure, we can plug both x and y back in to the left side of the OTHER equation (it won't work if you use the same one that you used to find x):
-5(3) + 7(2) simplifies to -15+14, which is -1. Since this does equal the right side of the equation, this means we have found x and y correctly.
If we had made a mistake, we would have gotten something that was not -1. What that means is that you have to go back and check your work. Two of the most common problems for these kind of equations is (a) forgetting to multiply the right side in the first step, and (b) forgetting negative signs.
Hope this helps.
Multiply the first equation by -5. We choose -5 because it is the coefficient of x in the second equation.
The first equation becomes
-20 + 15y = -30
Similarly, and for the same reason, multiply the second equation by 4.
It then becomes
-20x + 28y = -4
Now we will subtract these two equations by subtracting the expressions on the left sides of the equals signs, and then doing the same to the ones on the right sides. It is very important that the order of subtraction is the same for both right and left; that is, if you do [first]-[second] for the left sides, you have to do [first]-[second] again for the right side
In our case, that means
(-20x + 15y) - (-20x + 28y) = (-30) - (-4)
Distribute the negative signs:
-20x + 15y + 20x - 28y = -30 + 4
Combine like terms:
(-20+20)x + (15-28)y = -26
Simplify:
0x - 13y = -26
Simplify:
-13y = -26
Solve for y by dividing both sides by -13:
-13y/-13 = -26/-13
y = 2
Now we have found y.
Thus we can substitute y into any of the original equations. W'll pick the first one because it really doesn't matter which one we use:
4x - 3(2) = 6
Distribute:
4x - 6 = 6
Solve for x by first adding 6 to both sides...
4x - 6 + 6 = 6 + 6
4x = 12
...and then dividing by 4
4x/4 = 12/4
x = 3
Now we have found x.
If you want to be very sure, we can plug both x and y back in to the left side of the OTHER equation (it won't work if you use the same one that you used to find x):
-5(3) + 7(2) simplifies to -15+14, which is -1. Since this does equal the right side of the equation, this means we have found x and y correctly.
If we had made a mistake, we would have gotten something that was not -1. What that means is that you have to go back and check your work. Two of the most common problems for these kind of equations is (a) forgetting to multiply the right side in the first step, and (b) forgetting negative signs.
Hope this helps.