Use the provided image to find the solution to the …

Mathematics Questions

Step by Step Solution

Mathematics Questions

Use the image to answer the question. A coordinate plane with four quadrants shows the x- and y-axes ranging from negative 5 to 5 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is x minus 5 y equals 3. The equation of the dotted line is 3 x minus 2 y equals negative 4. The intersection of both lines is shown at negative 2 on the x-axis and negative 1 on the y-axis in quadrant 3. Review the graphs of a system of two linear equations in two variables: x√¢¬à¬í5y=7 and 3x√¢¬à¬í2y=√¢¬à¬í4. Find the solution to both equations.(1 point) The intersection point is ()

Short Answer

The solution to the system of equations x – 5y = 7 and 3x – 2y = -4 is found using the elimination method. After manipulating the equations, we determine that the intersection point is (216/13, -25/13).

Step-by-Step Solution

Step 1: Set Up the Equations

Start with the two linear equations given: x – 5y = 7 and 3x – 2y = -4. To prepare for the elimination method, we want to manipulate these equations so that we can eliminate one of the variables. The goal is to make the coefficients of either x or y equal, which can be achieved by multiplying the first equation.

Step 2: Apply the Elimination Method

Multiply the first equation by 3, giving us 3x – 15y = 21. Next, subtract the second equation (3x – 2y = -4) from this new equation. This leads to the simplified equation -13y = 25. From here, divide by -13 to isolate y, yielding y = -25/13.

Step 3: Solve for x and Find the Intersection Point

Now that we have y, substitute it back into the original equation x – 5y = 7. By replacing y with -25/13, we find: x = 7 + 125/13. Calculating this gives x = 216/13. Thus, the solution to the system of equations, or the intersection point, is (216/13, -25/13).

Related Concepts

Linear Equation

An equation that describes a straight line and can be represented in the form ax + by = c, where a, b, and c are constants and x and y are variables.

Elimination Method

A method for solving a system of linear equations by eliminating one variable by adding or subtracting the equations in order to solve for the remaining variable.

Intersection Point

The point where two or more lines (or equations) cross, representing the solution to the system of equations, which gives the values of the variables that satisfy all the equations simultaneously.

Table Of Contents

Use the image to answer the question. A coordinate plane with four quadrants shows the x- and y-axes ranging from negative 5 to 5 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is x minus 5 y equals 3. The equation of the dotted line is 3 x minus 2 y equals negative 4. The intersection of both lines is shown at negative 2 on the x-axis and negative 1 on the y-axis in quadrant 3. Review the graphs of a system of two linear equations in two variables: x√¢¬à¬í5y=7 and 3x√¢¬à¬í2y=√¢¬à¬í4. Find the solution to both equations.(1 point) The intersection point is ()