-3x-2y=-24
4x-7y=3
oobleck
answered
-12x - 8y = -96
12x - 21y = 9
add to get
-29y = -87
y = 3
Or, using substitution, since x = (2y-24)/3,
4(2y-24)/-3 - 7y = 3
4(2y-24) + 21y = -9
8y-96+21y = -9
29y = 87
y=3
Step-by-Step Bot
answered
Step 1: Multiply the first equation by 4 and the second equation by -3 to eliminate the x term.
-3x - 2y = -24 --> -12x - 8y = -96
4x - 7y = 3 --> -12x + 21y = -9
Step 2: Add the two new equations together to eliminate the x term.
(-12x - 8y) + (-12x + 21y) = -96 + (-9)
-24x + 13y = -105
Step 3: Solve the resulting equation for y.
13y = -24x - 105
y = (-24x - 105) / 13
Step 4: Substitute the value of y into one of the original equations. Let's use the first equation.
-3x - 2((-24x - 105) / 13) = -24
-3x - (48x + 210) / 13 = -24
-39x - 48x - 210 = -24(13)
-87x - 210 = -312
Step 5: Solve for x.
-87x - 210 = -312
-87x = -312 + 210
-87x = -102
x = (-102) / (-87)
x = 6 / 29
Step 6: Substitute the value of x back into one of the original equations to find y. Let's use the second equation.
4(6/29) - 7y = 3
24/29 - 7y = 3
- 7y = 3 - 24/29
- 7y = 87/29 - 24/29
- 7y = 63/29
y = (63/29) / (-7)
y = -9/29
Therefore, the solution to the system of equations is x = 6/29 and y = -9/29.
Explain Bot
answered
Step 1: Solve one equation for one variable in terms of the other variable. Let's solve the first equation for x.
-3x - 2y = -24
-3x = 24 - 2y
Divide both sides by -3:
x = (24 - 2y) / -3
Step 2: Substitute the expression for x into the other equation.
4x - 7y = 3
4((24 - 2y) / -3) - 7y = 3
Multiply both sides by -3 to eliminate the fraction:
4(24 - 2y) - 7y(-3) = 3(-3)
Simplify:
-96 + 8y + 21y = -9
Combine like terms:
29y - 96 = -9
Add 96 to both sides:
29y = 87
Divide both sides by 29:
y = 3
Step 3: Substitute the value of y back into the expression for x.
x = (24 - 2y) / -3
x = (24 - 2(3)) / -3
x = (24 - 6) / -3
x = 18 / -3
x = -6
Therefore, the solution to the system of equations is x = -6 and y = 3.
