Use elimination to solve.
X+5y=17
-4x+3y=24
multiply top equation by 4
4x+20y=68
-4x+3y=24
add the equations, solve for y (I get y=4), then use either equation to solve for x
To solve the system of equations using elimination, you need to eliminate one of the variables by multiplying one or both of the equations by suitable constants so that the coefficients of either x or y will add up to zero when you add the equations together.
Let's solve the system of equations:
1) X + 5y = 17
2) -4x + 3y = 24
To eliminate one of the variables, we can multiply equation 2 by a constant to make the coefficient of y equal to 5 (to match the coefficient of y in equation 1).
Let's multiply equation 2 by 5:
5 * (-4x + 3y) = 5 * 24
-20x + 15y = 120
Now we have two equations:
1) X + 5y = 17
3) -20x + 15y = 120
Next, we will add equation 1 and equation 3 together in order to eliminate y:
(X + 5y) + (-20x + 15y) = 17 + 120
X - 20x + 5y + 15y = 137
-19x + 20y = 137
Now we have a new equation:
4) -19x + 20y = 137
We can solve this equation for x or y to find its value and substitute it back into one of the original equations to solve for the other variable.
However, let's use elimination again to eliminate x. To do that, let's multiply equation 2 by 19 to make the coefficient of x equal to 20 (to match the coefficient of x in equation 4).
19 * (-4x + 3y) = 19 * 24
-76x + 57y = 456
Now we have two equations:
4) -19x + 20y = 137
5) -76x + 57y = 456
Next, we will add equation 4 and equation 5 together in order to eliminate x:
(-19x + 20y) + (-76x + 57y) = 137 + 456
-19x -76x + 20y + 57y = 593
-95x + 77y = 593
Now we have a new equation:
6) -95x + 77y = 593
We have successfully eliminated both variables except for y. Now, we can solve equation 6 for y:
-95x + 77y = 593
77y = 95x + 593
y = (95/77)x + (593/77)
Now we have the value of y in terms of x. We can substitute this into one of the original equations - let's use equation 1:
X + 5y = 17
X + 5((95/77)x + (593/77)) = 17
Simplifying this equation will give you the value of x. Substitute the value of x back into the equation we derived for y to find its value.
Lastly, you can check the values of x and y by substituting them into either of the original equations to ensure they satisfy the system.