Final answer:
To solve the system of equations, set them equal to each other to find x = 3. Then, substitute x into one of the equations to find y = 4. The solution of the system is (3, 4).
Step-by-step explanation:
To solve the system of equations, we need to find a pair of x and y values that satisfy both equations simultaneously. The equations given are:
y = 3x - 5
y = -2x + 10
We can set the two equations equal to each other since they both equal y.
3x - 5 = -2x + 10
By adding 2x to both sides and adding 5 to both sides, we get:
3x + 2x = 10 + 5
5x = 15
Dividing both sides by 5, we find that x equals 3.
x = 3
To find the corresponding value of y, we can substitute x into either of the original equations. Let's use the first equation:
y = 3(3) - 5
y = 9 - 5
y = 4
Therefore, the solution to the system of equations is (3, 4).