3x + 4y = -2 and 2x - 3y = 10
many ways to solve this: substitution, graphing, system of equations, etc.
I prefer system of equations, so here you go!
2(3x + 4y = -2) 6x + 8y = -4
3(2x - 3y = 10) -(6x - 9y = 30)subtract
17y = -34
y = -2
plug in -2 for y into one of the equations and solve...
3x + 4(-2) = -2
3x=6
x=2
Are we finding the intersection of these two lines ???
if so then
multiply the 1st by 3 ---> 9x + 12y = -6
multiply the 2nd by 4 ---> 8x - 12y = 40
add them
17x = 34
x = 2
plug that into the 1st
3(2) + 4y = -2
4y = -8
y = -2
x = 2, y = -2
To find the solution to the system of equations, we can use the method of substitution or elimination.
Let's solve this system of equations using the method of substitution:
1. Start with the first equation: 3x + 4y = -2.
2. Solve this equation for x in terms of y.
Subtract 4y from both sides: 3x = -2 - 4y.
Divide both sides by 3: x = (-2 - 4y) / 3.
Now we have x expressed in terms of y.
3. Substitute this expression for x into the second equation: 2((-2 - 4y) / 3) - 3y = 10.
Simplify this equation: (-4 - 8y) / 3 - 3y = 10.
4. Multiply through by 3 to get rid of the fraction: -4 - 8y - 9y = 30.
Combine like terms: -4 - 17y = 30.
5. Add 4 to both sides: -17y = 34.
6. Divide both sides by -17: y = -2.
We have found the value for y.
Now that we know y = -2, we can substitute this value back into one of the original equations to find x:
Using the first equation: 3x + 4(-2) = -2.
Simplify this equation: 3x - 8 = -2.
Add 8 to both sides: 3x = 6.
Divide both sides by 3: x = 2.
Therefore, the solution to the system of equations is x = 2 and y = -2.