Systems of Equations & Inequalities Review

A system of two linear equations has no solutions. The first equation is $$10x+7y=1$$ . What could be the 2nd equation that would make this system have no solution?

The graph of $$y=\frac{1}{2}x+5$$ is shown on the graph. Graph the equation $$y=-\frac{5}{2}x-1$$ on the same coordinate plane. Plot the point that represents the solution to the system consisting of the two equations.

Solve the system.

$$-x+3y=-6$$

$$-5x+3y=6$$

A linear equation is graphed on the coordinate grid.

When graphed on the same coordinate grid, which equation results in a system of equations with exactly one solution?

A system of equations is given below.

$$-5x+6y=25$$

$$-7x+8y=33$$

What is the value of y for the solution to the system? Type your response.

A linear equation is graphed on the coordinate grid.

When graphed on the same grid, which equation results in a system of equations with exactly one solution?

Solve the following system for y:

$$-7x-4y=29$$

$$3x-y=-7$$

The graphs of 3 systems of equations are shown. Drag an ordered pair to each box to identify the solution to each system.

One number, x, is 15 more than twice another number, y. The sum of the numbers is 75. What are the numbers?

Xoe took a total of 270 nickels and dimes to trade in for cash at the bank. She got exactly $21 back. How many dimes did she have?