To determine how many solutions this system has, we need to analyze the two equations given.
The first equation is:
-3x + 67 = 10
Let's solve for x:
-3x = 10 - 67
-3x = -57
x = -57 / -3
x = 19
Now we know the value of x.
The second equation is:
-3x + 6y = -4
Let's substitute the value of x we found (x = 19) into this equation:
-3(19) + 6y = -4
-57 + 6y = -4
Now, we solve for y:
6y = -4 + 57
6y = 53
y = 53 / 6
y = 8.8333...
Given that these are two linear equations with two variables, we would typically expect there to be a single solution unless the lines are parallel (no solutions) or the same line (infinitely many solutions). Since we were able to find a specific solution (x = 19, y ≈ 8.8333), it means the lines intersect at exactly one point, and there is one unique solution to this system of equations.
how many solutions does this system have?
-3x + 67 = 10
-3x + 6y = -4
1 answer