Multiply top equation by 3, bottom by 2 and eliminate y. Solve for x: -47/14=-3.357. Substitute x back into top equation to solve for y: -9.142. Thus, x=-3.357 and y=-9.142.
Write down the system of equations.
We're given the following system of equations:
y = 6x - 11
-2x - 3y = -7
Multiply the top equation by 3.
This will help us eliminate y in the next step.
18x - 33y = -33
-2x - 3y = -7
Multiply the bottom equation by 2.
This will make the coefficients of y in both equations easier to work with.
18x - 33y = -33
-4x - 6y = -14
Add the top and bottom equations together.
This eliminates y and leaves us with an equation in terms of x.
14x - 39y = -47
Solve for x.
Divide both sides of the equation by 14 to isolate x.
14x = -47
x = -47/14
x = -3.357
Substitute the value of x back into one of the original equations to solve for y.
We can use either of the original equations, but it's usually easiest to use the one with a simpler coefficient for x. Let's use the top equation:
y = 6x - 11
y = 6(-3.357) - 11
y = -20.142 + 11
y = -9.142
Write down the solution.
The solution to the system of equations is:
x = -3.357
y = -9.142