Review the graphs of a system of two linear equations in two variables: 4x+3y=15 and y=x+5 . Find the solution to both equations.
(1 point)
To find the solution to both equations, we can solve them simultaneously by using the method of substitution or elimination.
Using substitution:
1. Start with the equation y = x + 5.
2. Substitute this expression for y in the other 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 this value back into the equation y = x + 5: y = 0 + 5.
8. Simplify: y = 5.
So the solution to the system of equations is x = 0 and y = 5.
The graphs of the two equations represent lines in a coordinate plane. The first equation, 4x + 3y = 15, can be rewritten in slope-intercept form as y = -4/3x + 5. This equation represents a line with a slope of -4/3 and a y-intercept of 5. The second equation, y = x + 5, represents a line with a slope of 1 and a y-intercept of 5.
The solution to the system of equations is the point of intersection between these two lines, which is (0, 5).