-2x+6y=6
-7x+8y=-5
multiply the top by positive 8 and multiply the bottom by negative 6. then cancel out the y's and solve for x. plug x back into anyone and solve for y.
hmm. sounds like elimination to me.
For substitution, pick either equation and solve for x (or y):
-2x+6y=6
6y = 2x+6
y = x/3 + 1
Now substitute that into the other equation:
-7x+8y = -5
-7x + 8(x/3 + 1) = -5
-7x + 8x/3 + 8 = -5
-13x/3 = -13
x = 3
so, y = x/3+1 = 2
be sure to plug (3,2) into the original equations to make sure you (or I!) didn't make a mistake.
To solve this system of equations, we can use the method of elimination or substitution. I will explain both methods so you can choose which one you prefer.
Method 1: Elimination
Step 1: Multiply both sides of the first equation by 7, and multiply both sides of the second equation by 2 to make the coefficients of x in both equations the same.
-14x + 42y = 42
-14x + 16y = -10
Step 2: Now subtract the second equation from the first equation to eliminate the x term.
(-14x + 42y) - (-14x + 16y) = 42 - (-10)
-14x + 42y + 14x - 16y = 42 + 10
26y = 52
Step 3: Divide both sides of the equation by 26 to solve for y.
26y/26 = 52/26
y = 2
Step 4: Substitute the value of y back into one of the original equations and solve for x.
-2x + 6(2) = 6
-2x + 12 = 6
-2x = 6 - 12
-2x = -6
x = 3
The solution to the system of equations is x = 3, y = 2.
Method 2: Substitution
Step 1: Solve one of the equations for one variable in terms of the other variable.
From the first equation, we can solve for x:
-2x + 6y = 6
-2x = 6 - 6y
x = (6 - 6y)/(-2)
x = -3 + 3y
Step 2: Substitute the expression for x in the second equation.
-7(-3 + 3y) + 8y = -5
21 - 21y + 8y = -5
21 - 13y = -5
Step 3: Solve for y.
21 - 13y = -5
-13y = -5 - 21
-13y = -26
y = 2
Step 4: Substitute the found value of y back into one of the equations to solve for x.
-2x + 6(2) = 6
-2x + 12 = 6
-2x = 6 - 12
-2x = -6
x = 3
Again, the solution to the system of equations is x = 3, y = 2.
Both methods lead to the same solution. Choose the method that you find more intuitive or convenient for you to use.