Review the graphs of a system of two linear equations in two variables: x - 5y = 7 and 3x - 2y = - 4 Find the solution to both equations. (1 point) The intersection point is (
Right answer
(3, 2)
To find the solution to both equations, we need to graph them and look for the intersection point.
First, let's rearrange both equations into slope-intercept form (y = mx + b).
Equation 1: x - 5y = 7
Rearranging, we get y = (1/5)x - 7/5
Equation 2: 3x - 2y = -4
Rearranging, we get y = (3/2)x + 2
Now, let's plot the graphs of these equations:
Graph 1:
The equation y = (1/5)x - 7/5 represents a line with a slope of 1/5 and y-intercept of -7/5.
From the y-intercept, move 1 unit up and 5 units to the right to plot another point.
Draw a straight line passing through both points.
Graph 2:
The equation y = (3/2)x + 2 represents a line with a slope of 3/2 and y-intercept of 2.
From the y-intercept, move 3 units up and 2 units to the right to plot another point.
Draw a straight line passing through both points.
Now, find the intersection point by looking at where the two lines intersect on the graph.
The intersection point is approximately (2, -1).
Therefore, the solution to both equations is x = 2 and y = -1.
To find the solution to a system of two linear equations, you can use either the method of substitution or the method of elimination. Both methods involve manipulating the equations to isolate one variable and then solve for it.
Let's use the method of elimination to solve the given system of equations:
Equation 1: x - 5y = 7
Equation 2: 3x - 2y = -4
To eliminate one variable, we need to multiply one or both equations by a constant so that the coefficients of the variable are additive inverses (i.e., their sum equals zero). In this case, we can multiply Equation 1 by 2 and Equation 2 by 5:
2(x - 5y) = 2(7) --> 2x - 10y = 14
5(3x - 2y) = 5(-4) --> 15x - 10y = -20
Now we have two equations with the same coefficient for the variable y. We can subtract the first equation from the second equation to eliminate y:
(15x - 10y) - (2x - 10y) = -20 - 14
15x - 10y - 2x + 10y = -34
13x = -34
Dividing both sides by 13, we find:
x = -34/13
Now, substitute this value of x into either of the original equations to solve for y. Let's use Equation 1:
x - 5y = 7
(-34/13) - 5y = 7
Multiply both sides by 13 to eliminate the fraction:
-34 - 65y = 91
-65y = 91 + 34
-65y = 125
Dividing both sides by -65:
y = 125/-65
y = -25/13
So, the solution to the given system of equations is x = -34/13 and y = -25/13. The intersection point of the two graphs is (-34/13, -25/13).