For the first system of equations:
To solve this system of equations, we can use the method of substitution. We already have the equation y = 3x - 2. We can substitute this expression for y in the second equation and solve for x:
2x + 3(3x - 2) = 16
2x + 9x - 6 = 16
11x = 22
x = 2
Now, substitute the value of x back into the first equation to solve for y:
y = 3(2) - 2
y = 6 - 2
y = 4
Therefore, the first system of equations has one solution.
For the second system of equations:
To solve this system of equations, we can set the two equations equal to each other:
2x - 2y - 4 = x + 2
Now, solve for x:
2x - x = 2y + 2 + 4
x = 2y + 6
Substitute this expression for x into the second equation:
y = 2y + 6 + 2
y = 2y + 8
Rearrange this equation:
0 = y + 8 - 2y
0 = -y + 8
y = 8
Now, substitute the value of y back into the expression for x:
x = 2(8) + 6
x = 22
Therefore, the second system of equations has one solution.
For the third system of equations:
The two equations are y = -2x - 7 and y = -2x + 3. These equations have the same slope (-2), but different y-intercepts (-7 and 3). When two lines have the same slope and different y-intercepts, they are parallel and will never intersect. Therefore, the third system of equations has no solutions.
solve each system of equations on the left. Match the system to the correct number of solutions
y=3x-2. 2x+3y=16. (one solution, infinite solutions, or no solutions?)
2x-2y+-4. y=x+2. (one solution, infinite solutions, or no solutions?)
y=-2x-7. y=-2x+3. (one solution, infinite soulutions, or no solutions?)
1 answer