Answer: x = 1
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Step-by-step explanation:
Subtract the equations straight down.
- The x terms subtract to 3x - (-2x) = 3x+2x = 5x
- The y terms go away because y-y = 0
- The right hand sides subtract to 9-4 = 5
After that set of subtractions, we get the new equation 5x = 5.
It solves to x = 1 when dividing both sides by 5.
We can stop here since we found the x coordinate of the solution.
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If you want the y coordinate then plug this into either equation to solve for y
So,
3x+y = 9
3*1+y = 9
3+y = 9
y = 9-3
y = 6
Therefore, the two lines intersect at the solution point (x,y) = (1,6)
I recommend using a graphing tool like Desmos or GeoGebra to confirm.
If we used the other equation, then,
-2x+y = 4
-2*1+y = 4
-2+y = 4
y = 4+2
y = 6
We get the same y value from earlier. This helps verify the answer is correct.