We will explain both ways and show work of both. When we solve these equations, they are asking to find an intersection point.
Substitution: Make an equation equal to a variable, then plug this equation inside the other equation in the variable you made it equal to.
2x+y=1
3x+4y=14
1. We can make it equal to any variable, either x or y, and which ever equation, but let's make the first equation equal to y since it is much easier.
2x+y=1
-2x -2x
y=1-2x
2. Now that we rearranged this equation equal to y, let's plug this equation into the other equation in the y variable.
3x+4(1-2x)=14
3. Simplify and solve.
3x+4-8x=14 (Distribute the 4)
-5x+4=14 (Combine like terms)
-4 -4
-5x=10 (Isolate x)
x=-2
4. Plug in the x value into either equation to find the y coordinate.
x=-2
I'm going to plug this in the first equation.
2(-2)+y=1
-4+y=1
y=5
The answer is (-2,5)
Elimination: we get rid of one variable to easily get a x or y coordinate.
2x+y=1
3x+4y=14
How do we eliminate a variable? Think of this problem as an addition problem. Let's get rid of y since it looks easier. What multiplied by y plus the 4y in the row would make it equal to zero? This is eliminating the y variable.
1. By multiplying the first equation by negative 4, we will be able to eliminate y.
-4(2x+y=1)
3x+4y=14
2. Let's distribute.
-8x-4x=-4
3x+4y=14 (nothing is done to the second equation)
3. Add down.
-8x-4y=-4
3x+4y=14
_________
-5x+0=10
4. Solve for x
-5x=10
x=-2
5. Input the number in for an equation to get a coordinate.
I'm going to use the first equation since it's easier.
2(-2)+y=1
-4+y=1
y=5
The answer is (-2, 5)