4x + 3y = 15 and y = x + 5
find the solution to both equations
the intersection point is
(2,7)
To find the solution to both equations, we can substitute the expression for "y" from the second equation into the first equation. This will give us a new equation with only one variable, which we can then solve.
Substituting y = x + 5 into the first equation:
4x + 3(x + 5) = 15
Simplifying the equation:
4x + 3x + 15 = 15
7x + 15 = 15
7x = 0
x = 0
Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y.
Using the second equation, y = x + 5, and substituting x = 0:
y = 0 + 5
y = 5
Therefore, the intersection point is (0, 5).
To find the solution to both equations, you need to substitute the value of y from the second equation into the first equation. Let's solve the system of equations using the given information:
1) Start with the second equation: y = x + 5.
2) Substitute this value of y into the first equation: 4x + 3(x + 5) = 15.
3) Simplify the equation: 4x + 3x + 15 = 15.
4) Combine like terms: 7x + 15 = 15.
5) Subtract 15 from both sides: 7x = 0.
6) Divide both sides by 7: x = 0.
7) Substitute the value of x back into the second equation to find y: y = 0 + 5 = 5.
Therefore, the solution to both equations is x = 0 and y = 5. The intersection point is (0, 5).