Question

5.) is (-1, 3) a solution for the system of linear equations below?
-2x + 4y = 14 and -3y + 2x = 10
6.) is (2, 1) a solution for the system of linear equations below?
y = 3x - 5 and y = 5x - 8
7.) is (-2, -6) a solution for the system of linear equations below?
y + 8 = -1x and y - 2x = -2
8.) is (1, 0) a solution for the system of linear equations below?
y + 3x = 3 and y - 1x = -1
9.) is (2, -4) a solution for the system of linear equations below?
2y = -2x - 4 and 2y = 2x - 12
10.) is (-4, 1) a solution for the system of linear equations below?
-5x + 3y = -17 and -9x + 2y = 38

Explanation:

Problem 5: Is \((-1, 3)\) a solution?

Step1: Substitute into first equation

Substitute \(x = -1\), \(y = 3\) into \(-2x + 4y = 14\):
\(-2(-1) + 4(3) = 2 + 12 = 14\).

Step2: Substitute into second equation

Substitute \(x = -1\), \(y = 3\) into \(-3y + 2x = 10\):
\(-3(3) + 2(-1) = -9 - 2 = -11
eq 10\).

Step1: Substitute into first equation

Substitute \(x = 2\), \(y = 1\) into \(y = 3x - 5\):
\(1 = 3(2) - 5 = 6 - 5 = 1\).

Step2: Substitute into second equation

Substitute \(x = 2\), \(y = 1\) into \(y = 5x - 8\):
\(1 = 5(2) - 8 = 10 - 8 = 2
eq 1\).

Step1: Substitute into first equation

Substitute \(x = -2\), \(y = -6\) into \(y + 8 = -x\):
\(-6 + 8 = 2\), \(-(-2) = 2\).

Step2: Substitute into second equation

Substitute \(x = -2\), \(y = -6\) into \(y - 2x = -2\):
\(-6 - 2(-2) = -6 + 4 = -2\).

Answer:

No

Problem 6: Is \((2, 1)\) a solution?