Answer:
x = 2, y = 2
Explanation:
To do these:
- Solve one of the equations for one of the variables.
- Substitute that expression into the other equation
- Find what the other variable equals. It'll be a number.
- Put that number into either equation to find the other variable.
It doesn't matter which equation or variable you choose.
But sometimes one equation is simpler to solve for one variable. In this case, they're both about the same complexity:
3x - y = 4 --> y = 3x - 4
x + 2y = 6 --> x = -2y + 6
I like "y = 3x - 4" a little better because its x term is positive.
Plug that into the other equation for y:
x + 2y = 6 substitute the expression we found for y:
x + 2(3x -4) = 6 --> x + 6x - 8 = 6 --> 7x = 14 --> x = 2
Notice how powerful that technique is: we used one equation to find what y equals in terms of x. Then we plugged that into the other equation and were left with an equation with only x terms. We solved it to find out what number x must be.
Now that we know what number x is, we simply plug that into either equation and find y. The 2nd equation is a bit easier to work with:
x + 2y = 6 Plug in what we know (x = 2):
2 + 2y = 6 --> y = 4/2 = 2 Both x and y equal 2.
Check our work by putting those values into either equation:
x + 2y = 6 --> 2 + 2(2) = 6 --> 2 + 4 = 6
That's true, so our answers must be correct.